DOCUMENT RESUME

ED 119 723 IR 003 195

TITLE 16mm Film and Videotape'Lectures and Demonstrations. 1976/1977 COalog. INSTITUTION Massachusetts Inst. of Tech., Cambridge. Center for Advanced Engineering Study. PUB DATE 76 NOTE 101p. AVAILABLE FROM Massachusetts Institute of Technology, Center for Advanced Engineering Study, Cambridge, Massachusetts 02139

EDRS PRICE MF-$0.83 HC -$6.O1 Plus Postage DESCRIPTORS Artificial Intelligence; Calculus; *Catalogs; Chemistry; Computer Science; Economics; Electronics; Engineering; Experiments; Higher Education; *Instructional Films; Mathematics; Physics; Probability Theory; *Sciences; Statistics; Systems Analysis; Thermodynamics; *Video Tape Recordings IDENTIFIERS Massachusetts Institute of Technology

ABSTEACT The Massachusetts Institute of Technology provides a catalog of 16mm filmed and videotaped lectures and demonstrations. Each listing includes title, short description, length of presentation, catalog number, purchase and rental prices, and indications as to whether the item is film or videotape and black-and-white or color. The catalog is divided into 17 categories: artificial intelligence; calculus; colloid and surface chemistry; computer languages; digital signal processing; economics; engineering economy; friction, wear, and lubrication; introduction to experimentation; mechanics of polymer processing; modern ; network analysis and design; nonlinear vibrations; probability; random processes; thermostatics and thermodynamics; and special programs. Ordering information and forms are included. (LS)

*********************************************************************** * Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality * * of the microfiche and hardcopy reproductions ERIC makes available * * via the ERIC Document Reproduction Service (URS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original. *********************************************************************** Massachusetts Institute of Technology 16mm Film and Videotape Lectures and U.S. DEPARTMENT OF HEALTH, Demonstrations EDUCATION & WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO- DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN. 1976/1977 ATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF Catalog EDUCATION POSITION OR POLICY

Artificial Intelligence 2

Calculus 6

Colloid and Surface Chemistry 23 The Massachusetts. Institute of Technology has developed more Computer Languages 32 than 450 videotapes and 16 mm films on the sciences, mathemat- ics, engineering, and management. Digital Signal Processing 37 Produced at the Center for Advanced Engineering Study in Economics 41 cooperation with MIT and other faculty members, these programs were created as part of a self- Engineering Economy 45 study project for practicing engineers, industrial scientists, and technical managers. Friction, Wear, and Lubrication 48 Flexibly designed to meet indi- vidual learner needs, these 51 lectures and demonstrations will Introduction to Experimentation be useful to industry and on- campus graduate and undergraduate Mechanics of Polymer Processing 54 classes. Detailed study guides, including Modern Control Theory 60. lecture notes, reading assign- ments, problem sets, and solutions accompany most of the subjects. Network Analysis and Design 70 Descriptions of the films and videotapes follow. Please Nonlinear Vibrations 74 note the substantial discounts for complete set rental or purchase. Reservation forms Probability ,78 are included to facilitate your ordering. Random Processes 86

Thermostatics and Thermodynamics' 93

Special Programs 96 Artificial Intelligence Patrick H. Winston

Artificial Intelligence is the researchers believe that intelli- -science of making computers smart. gence is the product of a family It is practiced both by those who Of qualities that can be studied want to make computers more abstractly and without concern useful and by those who want to for the particular hardwareor understand the nature of intel- "brainware" machines that manifest ligence. intelligence. Intelligent systems will be better because they will know why some- Patrick H. Winston is Associate thing is wanted as well as what Professor of Computer Science at is wanted. But, making machines MIT and Director of the MIT Arti- smart is also a new kind of psy- ficial Intelligence Laboratory. chology. Artificial Intelligence

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2 3 Artificial Intelligence

Twenty-four Perceptrons and Hill Climbing Color Videotapes The perceptron idea. The in- ability of perceptrons to recog- Geometric Analogy Problems (1) nize connectivity. Learning Purposeful descriptions. through parameter twiddling. Symbolic pattern matching. Foothill, ridge, and plateau Descriptions of relations and problems. The need for layers of transformations. Rule comparison. information processing. 26-min. Color Videotape 34-min. Color Videotape 17-0101 Purchase $245 Rental $25. 17-0106 Purchase $300 Rental $30..

Picking The Next Move Geometric Analogy Problems (2) The mini-max method of game Geometric analogy examples. Re- playing. The alpha-beta speedup marks on improving performance. algorithm. Heuristic pruning. The role of analogy in identify- Static evaluation and plausible ing unknown objects. move generation. 20-min. Color Videotape 39-min. Color Videotape 17-0102 Purchase $200 Rental $20. 17-0107 Purchase $325 Rental $33.

The General Problem Solver Using Evidence Using goals and subgoals. Dif- Remarks on strategy and tactics. ference descriptions, operators, Learning to play better. Linear and conditions. Iteration, ee- scoring sums. Signature tables cursion, and automatic backup. and layered signature tables. Traveling to Aunt Agatha's. 25-min. Color Videotape 39-min. Color Videotape 17-0108 Purchase $240 Rental $24. 17-0103 Purchase $325 Rental $33.

Probing A New Domain Solving Calculus Problems (1) The problem of line drawing Goal trees and heuristic search. analysis. Combining regions in- Judging difficulty and focusing to bodies. More evidence versus attention. Strong and weak better evidence. Line drawing transformations. analysis as a research paradigm. 25-min. Color Videotape 44-min. Color Videotape 17-0104 Purchase $240 Rental $24. 17-0109 Purchase $350 Rental $35.

Solving Calculus Problems (2) Exploiting Constraints Alternatives in performance Identifying illegal drawings. measurement. Depth-first, Classification of lines and ver- breadth-first, and environment- texes. Searching for compatible driven search. Using programs as and vertex interpretations. metaphors. The ephemeral quality of intelligence. 39-min. Color Videotape 17-0110 Purchase $325 Rental $33. 24-min. Color Videotape 17-0105 Purchase $230 Rental $23.

3 4 ARTIFICIAL INTELLIGENCE - Continued Working Out An Epistemology LISP Basics (2) Handling shadows and cracks. Free and bound variables. Using illumination information. MAPCAR, APPLY, and LAMBDA. Cal- Coping with small infinities. culating the depth of an S- The metatheory of description expression. Finding the mini- refinement. max value of a tree. 32-min. Color' Videotape 33-min. Color. Videotape 17-0111 Purchase $285 Rental $29. 17-0115 Purchase $290 Rental $29. Learning Description based learning of Differentiation in LISP structures from samples. The The identical form of programs importance of the near-miss. and data. Constructing new S- Model refinement using emphatic expressions'from pieces of old relations. Hypothesis and con- ones. Simplification on the tradiction. Learning by dis- fly. Intermediate expression covery, from examples, and by bulge. being told. 42-min. Color Videotape 28-min. Color Videotape 17-0116 Purchase $340 Rental $34. 17-0112 Purchase $260 Rental $26. Building A Matching Language Identifying Structures and Con- Using LISP text Storing and Retr:ieving in- Computing relations between ob- formation using property lists. jects. Plain and fancy ident- Matching patterns against known ification. Searching through facts. Storing facts in similarity networks. Frame indexed directories. systems and contexts. 43-min. Color Videotape 34-min. Color Videotape 17-0113 Purchase $345 Rental $35. 17-0117 Purchase $300 Rental $30.

LISP Basics (1) Improving The Matching Function Basic numeric and symbol- Simultaneous matching and manipulating primatives. Values variable assignment. Matching and properties. The need for pattern elements against quoting. Predicates and con- strings. Restricted matching. ditionals. Defining new .functions. Recursion. 30-min. Color Videotape 17-0118 Purchase $275 Rental $28. 20-min. Color Videotape 17-0114 Purchase $200 Rental $20.

ARTIFICIAL INTELLIGENCE -CompiNVSet

Color Videotapes Study Guide Complete set oftwenty-fourcolor Comments, photographs, refer- videotapes. ences, problems, solutions. 182 pp. (One per student 17-1100 Purchase $5825 (SAVE $940) recommended.) 120 Day Rental *607 (SAVE $74) 17-2100 Purchase $8.00 each. Suggested Text (10% Discount on five or more) The Psychology of Computer A Complete Serf-Study Subject. Vision, edited by P. H. Winston, The sat of videotapes described McGraw-Hill, 1975.282 pp. above can be wed as a complete seif- 17-3100 Purchase $18 each. studysubject when accompanied by the Study Guide and Suggested Text.

4 Working Algebra Word Problems Effecting English Commands in Translation of sentences into the Blocks World equations. Breaking up com- Goal oriented programming. The pound sentences. Retrieving heterarchical approach. Putting library facts. The toy the pyramid on the green block. psychiatrist program. 42-min. Color Videotape 41-min. Color Videotape 17-0122 Purchase $340 Rental $34. 17-0119 Purchase $335 Rental $34. Constraint Structures Demons and Automatic Backup Sets of mutually exclusive The MICRO-PLANNER Language. features. Entry conditions. Consequent, antecedant, and A 0th order theory of semantics. erasing subroutines. Looking Bouncing the pointed ball. for a fallible sinner. 23-min. Color Videotape 21-min. Color Videotape 17-0123 Purchase $220 Rental $22. 17-0120 Purchase $205 Rental $21. Aspects of Natural Language Syntax Understanding English Context free and transformation- The role of syntax, semantics, al grammars. Systemic grammar and deduction. The structure Translating and feature driven analysis. of noun groups. Special purpose languages for noun groups into MICRO-PLANNER dealing with syntax. Picking up programs. a big red box. 36-min. Color Videotape 31-min. Color Videotape 17-0121 Purchase $310 Rental $31. 17-0124 Purchase $280 Rental $28.

5 6 Calculus Herbert I. Gross

Calculus covers the material norm- part of the course covers complex ally found in the first two years variables, differential equations, of a modern college sequence in and linear algebra. calculus, differential equations, and linear algebra. The course Designed originally as a refresher begins with elementary set theory course (and, in fact, called and other aspects of "new math" Calculus "Revisited" when used at and continues with differential and MIT), this material is suitable for integral calculus, circular and all students with the requisite transcendental functions, and background. infinite series. The courathen continues with vector arithmetic and vector calculus, partial Herbert I Gross was Senior Lec- derivatives, matrix algebra, and turer, Massachusetts Institute of multiple integration. The final Technology.

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7 Calculus

Functions Preface to Calculus Notations; concepts of onto and An introduction to calculus; the one-to-one; the arithmetic of concept of 0/0; instantaneous functions of a real variable; speed; introduction to functiOns intervals and deleted neighbor- and graphs; the limit concept; hoods; absolute values; compo- area; general overview of calculus. sition of functions. 32-min. B&W Film or Videotape 39-min. B&W Film or Videotape 26-0000 Purchase $215 Rental $22. 26-0102 Purchase .$255 Rental $2f.

Inverse Functions, "Switch in Sets, Functions, and Limits Emphasis" The concept of an inverse func- Six B&W 16mm tion; some examples; graphical Films or Videotapes interpretation; single-valued Analytic Geometry and multi-valued functions; a Cartesian coordinates; curves as discussion of branches of func- sets of points; graphs of func- tions. tions; equations of straight 40-min. B&W Film or Videotape lines; simultaneous linear 26-0103 Purchase $260 Rental $26. equations. 37-min. B&W Film or Videotape 26-0101 Purchase $240 ,Rental $24.

SETS, FUNCTIONS, AND LIMITS - Complete Set

Films/Videotapes Study Guide Complete set of six B&W Pretest, reading assignments, 16 mm films or videotapes problems, solutions, quiz. 26-1100 Purchase $1600 (SAVE $140) 184 pp. (One per student 30 Day Rental $166 (SAVE $10) recommended.) 26-2100 Purchase $6.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, Lecture Notes Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs 26-3000 Purchase $16.95 each. for all the films/videotapes on Calculus of a Single Variable. Supplementary Notes 82 pp. A supplement to the text, cover- 26-5000 Purchase $4.50 each. ing "new math" concepts and expanding on difficult topics in A Complete Self-Study Subject. Calculus of a Single Variable. The set offilms/Videotapes described 346 pp. above can be used as a complete self- study subject when accompanied by 26-4000 Purchase $11.00 each. the Study Guide, Lecture Notes, Sug- gested Text, and Supplementary Notes.

7 8 SETS, FUNCTIONS, AND LIMITS - Continued

Derivatives and Limits Instantaneous speed as an out- Differentation growth and refinement of average speed; definition of limit; Eleven B&W 16mn instantaneous speed as a limit; Films or Videotapes the formal definition of limit Derivatives of Some Simple Functions and some consequences. Definition of derivative; the derivative of xn where n is an 45-min. B&W Film or Videotape integer; derivatives of sums, 26-0104 Purchase $285 Rental $29. differences, products, and quotients. A More Rigorous Approach to Limits 28-min. B&W Film or Videotape A continuation of the previous 26-0201 Purchase $190 Rental $20. lecture; important limit pro- perties are developed as theorems from the formal definition of Approximations and Infinitesimals limit. Approximating. Ay by f'(x)Ax; discussion of the difference 46-min. B&W Film or Videotape between Ay and f'(x)Ax; some 26-0105 Purchase $290 Rental $29. examples; introduction to the chain rule. Mathematical Induction 34-min. B&W Film or Videotape The meaning of mathematical 26-0202 Purchase $225 Rental $23. induction; some examples of what mathematical induction is and isn't; applications to limit Composite Functions and the theorems. Chain Rule Composition of functions; a. 29-min. B&W Film or Videotape graphical interpretation; applica- 26-0106 Purchase $195 Rental $20. tions to parametric equations; using the chain rule to extend our concept of finding derivatives. 39-min. B&W Film or Videotape 26-0203 Purchase $255 Rental $26.

DIFFERENTIATION - Complete Set

Films/Videotapes Study Guide Complete set of eleven B&W Pretest,-reading assignments, 16 mm films or videotapes. problems, solutions, quiz. 26-1200 Purchase $2135 (SAVE $240) 268 pp. (One per student 55 Day Rental $230 (SAVE $17) recommended.) 26-2200 Purchase $8.50 each. Suggested Text (10% Discount on five or more). Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, Lecture Notes. Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs 26-3000 Purchase $16.95 each. for all the films/videotapes on Calculus of a Single Variable. Supplementary Notes 82 pp. A supplement to the text, cover- 26-5000 Purchase $4.50 each. ing "new math" concepts and expanding on difficult topics in A Complete Self-Study Subject. Calculus of a Single Variable. The set of'films/Videotapes described 346 pp. above can be used as a complete self- study subject when accompanied by 26-4000 Purchase $11.00 each. the Study Guide Lecture Notes, Sug- gested Text,. and Supplementary Notes

8 Differentiation of Inverse Rolle's Theorem and its Functions Consequences The concept of an inverse function; Statement of Rolle's Theorem; a differentiation of an inverse func- geometric interpretation; some tion; when is a function invertible? cautions; the Mean Value Theorem; consequences of the Mean Value 28-min. B&W Film or Videotape Theorem. 26-0204 Purchase $190 Rental $20. 30-min. B&W Film or Videotape 26-0209 Purchase $205 Rental $21. Implicit Differentiation Finding the derivative when the Inverse Differentiation functional relationship is implied The "Opposite" of differentiation; (that is, when it has the form trying to find f(x) knowing f'(x); f(x,y) = 0]; application to the some examples; some formulas; case of xn where n is a rational notation. number; the use of implicit differentiation in the study of 42-min. B&W Film or Videotape 26-0210 Purchase $270 Rental $27. related rates. 40-min. B&W Film or Videotape The "Definite" Indefinite Integral' 26-0205 Purchase $260 Rental $26. b The meaning of Ji f(x) dx as Continuity Physical internretation of a continuity; th, of g(b) - g(a) where g'(x) = f(x); continuity in terms of limits; some applications. a geometric interpretation of 29-min. B&W Film or Videotape continuity; some applications 26-0211 Purchase $195 Rental $20. of continuity to equation solving; some analytic conse- quences of definition of The Circular Functions continuity. Two B&W 16mm Films or Videotapes 22-min. B&W Film or Videotape 26-0206 Purchase $150 Rental $20. Circular Functions Trigonometric functions without the use of angles; the logic of Curve Plotting radian measure; the definition of Basic pre-calculus review; even circular functions; the derivative of sin x and cos x. and odd functions and other . symmetries; the role of the first 35-min. B&W Film or Videotape and second derivatives in curve 26-0301 Purchase $230 Rental $23. plotting; stationary points; inflections; some examples. Inverse Circular Functions 31-min. B&W Film or Videotape Meaning of arcsin x in terms of the 26-0207 Purchase $210 Rental $21. sine function; the derivative of arcsin x in terms of the derivative of sin x; some applications. Maxima and Minima 26-min. B&W Film or Videotape High and low points of a curve; 26-0302 Purchase $175 Rental $20. techniques for finding these high and low points; applications to finding maxima and minima of func- Study Guide tions; some physical applications. Pretest, reading assignments, 34-min. B&W Film or Videotape problems, solutions, quiz. 26-0208 Purchase $225 Rental $23. 96 pp. (One per student recommended.) 26-2300 Purchase $4.00 each. (10% Discount on five or more.)

9 10 The Definite Integral 1-Dimensional Area The main difference between Four B&W 16mm arclength and either area or Films or Videotapes volume; the limit definition of The Definite Integral arclength; some philosophical and Axiomatic approach to area; area practical questions concerning approximations by upper and lower the definition; approximating bounds; the method of exhaustion; errors and their magnitude when using limits to find areas of non- we use infinite sums. rectilinear regions; piecewise 36-min. B&W Film or Videotape continuity; trapezoidal approxi- 26-0404 Purchase $235 Rental $24. mations. 36-min. B&W Film or Videotape 26-0401 Purchase $235 Rental $24. Transcendental Functions Marriage of Differential and Four B&W 16mm Integral Calculus Films or Videotapes First Fundamental Theorem of Logarithms without Exponents Integral Calculus, some applica- The concept of the natural tions; Second Fundamental Theorem logarithm; the notion of the rate of Integral Calculus; some of change being proportional to applications; significance of the the amount.,yeesent; the general two theorems. concept of'6: logarithmic function; 30-min. B&W Film or Videotape the study of ln x in terms of 26-0402 Purchase $205 Rental $21. differential calculus; the study of ln x in terms of integral calculus; the meaning of the 3-Dimensional Area number e as the base of the Extending the axioms of area to natural logarithms. volume; some applications; the 34-min. B&W Film or Videotape method of cylindrical shells. 26-0501 Purchase $225 Rental $23. 42-min. B&W Film or Videotape 26-0403 Purchase $270 Rental $27.

THE DEFINITE INTEGRAL - Complete Set

Films/Videotapes Study Guide Complete set.of four B&W Pretest, reading assignments, 16 mm Films or Videotapes. problems, solutions, quiz. 26-1400 Purchase $870 (SAVE $75) 128 pp. (One per student 20 Day Rental $ $86 (SAVE $10) recommended.) 26-2400 Purchase $4.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, Lecture Notes Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs 26-3000 Purchase $16.95 each. for all the films/videotapes on Calculus of a Single Variable. 82 pp. Supplementary Notes 26 -5000 Purchase $4.50 each. A supplement to the text, cover- ing "new math" concepts and A Complete Sell-Study Subject. expanding on difficult topics in The set of films/videotapes described Calculus of a Single Variable above can be used as a complete self- 346 pp. study subject when accompanied by the Study Guide, Lecture Notes, Sug- 26-4000 Purchase $11.00 each. gested Text, and Supplementary Notes.

10 11 Inverse Logarithms The invertibility of the More Integration Techniques logarithmic function; ex as the Four B&W 16mm inverse of In x; a discussion of Films or Videotapes exponential functions; some applications. Some Basic Recipes 21-min. B&W Film or Videotape A review and extension of previous 26-0502 Purchase $145 Rental $20. results for finding f(x) knowing f'(x); particular emphasis is placed on the case where f'(x) What a Difference a Sign Makes involves the sum and/or difference Hyperbolib functions in terms of of two squares; completing the the hyperbola x2-y2=1; compari- square. sons with the circular functions; 30-min. B&W Film or Videotape the relationship between hyperbolic 26-0601 Purchase $205 Rental $21. functions and exponential func- tions; applications of calculus to hyperbolic functions. Partial Fractions 27-min. B&W Film or Videotape The concept of partial fractions; 26-0503 Purchase $180 Rental $20. finding f(x) when f'(x) is the quotient of two polynomials; some notes about identities; application of partial fractions to the case Inverse Hyperbolic Functions where f is of the form The theory of inverse functions f(sin x, cos x). applied to the hyperbolic func- tions; some formulas for dif- 32-min. B&W Film or Videotape ferentiation and integration; some 26-0602 Purchase $215 Rental $22. applications. 30-min. B&W Film or Videotape 26-0504 Purchase $205 Rental $21.

TRANSCENDENTAL FUNCTIONS - Complete Set

Films/Videotapes Study guide Complete set of four B&W Pretest, reading assignments, 16 mm films or videotapes problems, sontions, quiz. 90 pp. (One per student 26-1500 Purchase $695 (SAVE $60) recommended.) 20 Day Rental $74 (SAVE $10) 26-2500 Purchase $1.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, Lecture Notes Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs for all the films/videotapes on 26-3000 Purchase $16.95 each. Calculus of a Single Variable. Supplementary Notes 82 pp. A supplement to the text, cover- 26-5000 Purchase $4.50 each. ing "new math" concepts and expanding on difficult topics in A Complete Self-Study Subject. Calculus of a Single Variable. The set of films/videotapes described above can-be used as a complete self- 346 pp. Study subject when accompanied by 26-4000 Purchase $11.00 each. the. Study Guide, Lecture Notes, Sug- gested Text, and Supplementary Notes.

11 12 MORE INTEGRATION TECHNIQUES - Continued

Integration by Parts Using the identity Infinite Series d(uv) = v + vdu to findJudy knowingvdu; using the technique Six B&W 16nrrn to evalu to certain integrals; Films or Videotapes reduction formulas; some Many Versus Infinite applications. Discussion of how infinity differs 26-min. B&W Film or Videotape from "very large"; some subtle and 26-0603 Purchase $175 Rental $20. not subtle consequences of the difference; the case against intuition; motivating infinite Improper Integrals series in terms of finding area The problem of trying to study as a limit. 26-min. B&W Film or Videotape If(x)dx when f(x) is not 26-0701 Purchase $175 Rental $20. continuous on the interval [a,b]; some examples; what happens if the Positive Series limits of integration are not The special case whereineach term finite; importance of improper in the series isnon-negative; the integrals. concept of convergence;the 29-min. B&W Film or Videotape comparison test; the ratiotest; 26-0604 Purchase $195 Rental $20. the integral test. 34-min. B&W Filmor VideOtape 26-0702 Purchase $225Rental $23.

MORE INTEGRATION TECHNIQUES- Complete Set

Films/Videotapes 11 Study Guide Complete set of fotr B&W Pretest, reading assignments, 16 mm films or videotapes. problems, solutions, quiz. 26-1600 Purchase $/25 (SAVE $65) 80 pp. (One per student 20 Day Rental $73 (SAVE $10) recommended.) 26-2600 Purchase $4.00 each. "Suggested Text AJA4 Discount on five or more.) Calculus and Analytic Geometry (Fourth gdition) by G.B Thomas, Lecture Notes Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs for all the films/videotapes on 26 -3000 Purchase $16.95 each. Calculus of a Single Variable. Supplementary Notes 80 pp. A supplement to the text, cover- 26-5000 Purchase $4.50 each. ing "new math" concepts and expanding on difficult topics in A Complete Self-Study Subject. Calculus of a Single Variable. The set of films/videotapes described 146 pp. above can be used as a complete self- study subject when accompanied by 26-4000 Purchase $11.00 each. the Stuck Guide,'Lecture Motes, Sug-, gested Text, and Supplementary Notes.

12 13 Absolute Convergence Uniform Convergence Discussion of non-absolute A discussion of pointwise con-

convergence; conditional and . vergence versus uniform con- absolute convergence; the vergence; some important subtlety of a series converging consequences of uniform con- When each of its negative terms vergence; applications of is replaced by the absolute value uniform convergence to the study of tha.t term; some consequences of power series. of absolute convergence; geometric 28-min. B&W Film or Videotape interpretation. 26-0705 Purchase $190 Rental $20. 21-min. B&W Film or Videotape 26-0703 Purchase $145 Rental $20. Uniform Convergence of Power Series Polynomial Approximations The topics introduced in the Using an nth degree polynomial to previous lecture are extended approximate a function f(x); how here. In particular the to choose the coefficients of the Weirstrass M-test is introduced polynomial to vet the "best" and discussed; using power series approximation; the notion of a to evaluate definite integrals power series; interval of when we do not know the anti- convergence of a power series; derivative of the integrand. Taylor's Remainder Theorem; expressing functions in terms of 27-min. B&W Film or Videotape 26-0706 Purchase $180 Rental $20. power series. 32-min. B&W Film or Videotape 26-0704 Purchase $215 Rental $22.

INFINITE SERIES - Complete Set

Films/Videotapes Study Guide Complete set of six B&W Pretest, reading assignments, 16 mm films or videotapes. problems, solutions, quiz. 178 pp.(One per student 26-1700 Purchase $1040 (SAVE $90) recommended.) 30 Day Rental $115 (SAVE $10) 26-2700 Purchase $6.00 each. Suggested Text (10% Discount on five or more.),, Calculus and Analytic Geometry Lectures Notes (Fourth Edition) by G.B. Thomas, Addison-Wesley, 1968, 818 pp. A set of chalkboard photographs for all the films/videotapes on 26 -3000 Purchase $16.95 each. Calculus of a Single Variable. 80 pp. Supplementary Notes 26-5000 Purchase $4.00 each. A supplement to the text, cover- ing "new math" concepts and A Complete Self -Study Subject. expanding on difficult topics in The set of films/videotapes described Calculus of a Single Variable. abo0e can be used as a complete saf 346 pp. study subject when accompanied by 26-4000 Purchase $11.00 each. the Study Guide, Lecture Notes, Sug- gested Text, and SUpplementary Notes.

14 13 The Dot Product sector Arithmetic Physical motivation in terms of Six B &W 16mm "work"; the geometric definition; Films or Vi.leotapes computing the dot product in Cartesian coordinates; the :.='The "Game" of Mathematics mathematical structure of the The generalized definition of a dot produCt; geometric applica- game; mathematics as a "game"; tions to finding angles and mathematical structure viewed as a "game". length projections. 29-min. B&W Film or Videotape 20-min. B&W Film or Videotape 27-0101 Purchase $140 Rental $20. 27-0104 Purchase $195 Rental $20.

"Arrow" Arithmetic The Cross Product Definition of a vector; vectors Geometric definition; the struc- as directed lengths (arrows); ture of the cross product; Mdition of vectors (the result- computing the cross product in antY;,i and j components; an Cartesian coordinates; using introduction to vector arithmetic determinant notation to compute in terms of mathematical struc- the cross product; geometric ture. applications of the cross 28-min. B&W Film or Videotape product to finding areas and 27-0102 Purchase $190 Rental $20. lines perpendicular to planes. 31-min. B&W Film or Videotape 3-Dimensional Vectors 27-0105 Purchase $210 Rental $21. Generalization from 2-dimensional space to 3-dimensional space; i,j, and k components of vectors; Equations of Lines and Planes Vector methods for finding the vector arithmetic in 3-dimensional equation of a line in 3-space; Cartesian coordinates; other finding the equation of coordinate systems; vector pro- a plane in terms of vectors;some perties versus coordinate pro- examples. perties. 28-min. B&W Film or Videotape 26-min. B&W Film or Videotape 27-0106 Purchase $190 Rental $20. 27-0103 Purchase $175 Rental $20.

VECTOR ARITHMETIC- Complete Set

Films/Videotapes Study Guide Complete set of six B&W Pretest, chalkboard photographs, 16 mm films and videotapes. reading a'Asignments, problems, 27-1100 Purchase $1010 (SAVE $90) solutions, quiz. 173 pp. (One 30 Day Rental $111 (SAVE $10) per student recommended.) Suggested Text 27-2100 Purchase $5.50 each. (10% Discount on fiveor more). Calculus and Analytic Geometry (Fourth Edition) by G.B.Thomas, A Complete Self -Study Subject. Addison-Wesley, 1968, 818pp. The set of-films /videotapes described above can be used asa complete self- 26-3000 Purchase $16.95 each. study subject when accompanied by the Study Guide, SuggePted Text, and Supplementary Notes Supplementary Notes. A supplement to the text intro- ducing the concept of mathematical structure and expanding on dif- ficult topics in Calculusof Several Variables. 182 pp. 27-4000 Purchase $5.00 each.

14 15 Polar Coordinates Vector Calculus Definition of polar coordinates; Four E37.,' 16mm the relationship between polar V-7:1e2tareo and Cartesian coordinates; polar equations for curves; slope and Vector Functions of a Scalar area in terms of polar Variable coordinates. Th6 concept of "operating" on a 30-min. B&W Film or Videotape number to produce a vector; 27-0203 Purchase $205 Rental $21. force as a function of time; limit theorems; the derivative of a vector function of a scalar Vectors in Polar Coordinates variable; some formulas for The basis vectors in polar finding derivatives; application coordinates; the need for using to motion in a plane. polar coordinates in some vector 38-min. B&W Film or Videotape problems; the position vector, 27-0201 Purchase $250 Rental $25. the velocity vector, and the acceleration vector in polar coordinates; applications to a Tangential and Normal Vectors central force field. The position vector; the unit 27-min. B&W Film or Videotape tangent vector; the unit normal 27-0204 Purchase $180 Rental $20. vector; the concept of curvature and radius of curvature; the torsion vector in 3-dimensional space. 28-min. B&W Film or Videotape 27-0202 Purchase $190 Rental $20.

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VECTOR CALCULUS - Complete Set

Films/Videotapes Complete Set of four B&W Study Guide 16 mm films and videotapes. Pretest, chalkboard photographs, 271200 Purchase $760 (SAVE $65) reading assignments, problems, 20 Day Rental $76 (SAVE $10) solutions, quiz. 212 pp. (One per student recommended.) Suggested Text 27-2200 Purchase $7.00 each. Calculus and Analytic Geometry (10% Discount on five or more). (Fourth Edition) by G.B. Thomas, Addison-Wesley, 1968, 818 pp. A Complete Self-Study Subject. The set of films/videotapes described 26-3000 Purchase $16.95 each. above can be used as a complete self- study subject when accompanied by Supplementary Notes - the Study Guide, Suggested Text, and A supplement to the text intro- Supplementary Notes. ducing the concept of mathematical structure and expanding on dif- ficult topics in Calculus of Several Variables. 182 pp. 27-4000 Purchase $5.00

15 16 Directional Derivatives Partial Derivatives Motion in a direction other than Six B&W 16mm parallel to either the x- or Films or videotapes y-axis; the definition of a n-Dimensional Vector Spaces. directional derivative in terms The concept of a vector as the of Cartesian coordinates; the independent variable; a scalar gradient vector; the tangent plane; some examples of function of a vector variable; the structure of an n-dimensional directional derivatives. vector space; an example of a 33-min. B&W Film or Videotape 4-dimensional vector space; 27-0303 Purchase $220 Rental $22':' generalizing the concepts of distance and limits to n-dimensional vector spaces. The Chain Rule Generalizing the Chain. Rule to a 32-min. B&W Film or Videotape function of several real 27-0301 Purchase $215 Rental $22. variables; using the chain rule to find higher order derivatives; some examples. Calculus of Several Variables The special case of 2 independent 38-min. B&W Film or Videotape variables; a geometric interpre- 27-0304 Purchase $250 Rental $25. tation; the concept of a partial derivative; some special cautions; the partial derivative in terms Integrals Involving Parameters of "slices" of a surface; the Physical motivation; geometric concept of a tangent plane to a interpretation; differentiating surface. ff(x,y) dy; variable limits of 35-min. B&W Film or Videotape 27-0302 Purchase $230 Rental $23. a integration; some subtleties. 27-min. B&W Film or Videotape 27-0305 Purchase $180 Rental $20.

PARTIAL DERIVATIVES - Complete Set

Films/Videotapes Study Guide Complete set of six B&W Pretest, chalkboard photographs, 16 mm films and videotapes reading assignments, problems, 27-1300 Purchase $1185 (SAVE $105) solutions, quiz. 306 pp. (One per student recommended.) 30 Day Rental $122 (SAVE $10) 27-2300 Purchase $10.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, A Complete Self-Study Subject. Addison-Wesley, 1968, 818 pp. The set offUms/videotapes described above can be used as a complete self- 26-3000 Purchase $16.95 each. study subject when accompanied by the Study Guide, S4ggested Text, and Supplementary Notes Supplementary Notes. A supplement to the text intro- ducing the concept of mathematical structure and expanding on dif- ficult topics in Calculus of Several Variables. 182 pp. 27-4000 Purchase $5.00 each.

16 17 Exact Differentials The "Game" of Matrices The differential of f(x,y); the n by n matrices; defining equality definition of the total dif- of two matrices; adding two ferential; the meaning of an matrices; -structural properties exact differential; applications of matrix arithmetic; some to equations of the form f(x,y)=0 differences tvtween matrix and numerical arithmetic; non- 29-min. B&W Film or Videotape singular matrices,;. introduction 27-0306 Purchase $195 Rental $20. to matrix algebra; using de- terminants to study non-singular matrices. Matrix Algebra 41-min. B&W Film' or Videotape 27-0402 Purchase $265 Rental $27. Five B&W 16mT Films or Videotapes Inverting a Matrix' Linearity Revisited Finding the inverse of a non- Properties of linear functions; the concept of "locally" linear singular matrix; interpretation in terms of matrix algebra, using the linear part ofw to study w = f(x,y) in "small" functions, and geometry; discus- sion of when a matrix is singular neighborhoods; systems of linear equations; matrix notation how to determine whether a matrix motivating matrix multiplication. Can be inverted. 45-min. B&W Film or Videotape 47-min. B&W Film or Videotape 27-0403 Purchase $285 Rental $29. 27-0401 Purchase $300 Rental $30. Inverting More General Systems of Equations A review of inverting linear systems; inverting more general (i.e., non-linear) systems; the Jacobian; some examples; discus- sion of various pitfalls. 28-min. B&W Film or Videotape 27-0404 Purchase $190 Rental $20.

MATRIX ALGEBRA - Complete Set

Films/Videotapes Study Guide Complete set of five B&W Pretest, chalkboard photographs, 16 mm films or videotapes . reading assignments, problems, solutions, quiz. 262 pp. (One 27-1400 Purchase $1165 (SAVE $100) per student recommened.) 25 Day Rental $119 (SAVE $10) 27-2400 Purchase $8.50 eacj. Suggested Text (10% Discount on five or afore.) Calculus and Analytic Geometry A Complete se*study subJect. (Fourth Edition) by G.B. Thomas, The setoffilme/videopapes described Addison-Wesley, 1968, 818 pp. above can be used asaacmplete self- 26-3000 Purchase $16.95 each. studysubject whamaccoMpanied by the Study (kids, Suggested Text, and Supplementary Notes Supplementary Notes. A supplement to the text intro- ducing.the concept of nathematical structure and expanding on dif- ficult topics in Calculus of Several Variables. 182 pp. 27-4000 Purchase $5.00 each.

17 18 MATRIX ALGEBRA - Continued

Maxima and Minima in Several The Fundamental Theorem Variables The anti-derivative in several The meaning of relative maxima and variables; some examples; a and minima in the study of real- geometric interpretation in term valued functions of several real of areas; computing limits of variables; how to test for such certain infinite double sums by values; a geometric interpreta- means of the anti-derivative and tion; constraints and the use conversely. of the chain rule. -26-min. B&W Film or Videotape 34-min. B&W Film or Videotape 27-0502 Purchase $175 Rental $20. 27-0405 Purchase $225 Rental $23. Multiple Integration and the Jacobian Multiple Integration A review of the definite integral and change of variable; an Five B&W 16mm example; the problem when we deal Films or Videotapes with more than one independent Double Multiple Sums variable; mapping a region of the xy-plane into a region in the Physical motivation in terms of uv-plane; the role of the Jacobian variable density; geometric in change of variable problems interpretation; application to involving multiple integration. finding the mass of asquare plate; upper and lower bounds; 33-min. B&W Film or Videotape generalization; multiple sum 27-0503 Purchase $220 Rental $22. notation limits involving multiple sums. Introduction to Line Integrals 30-min. B&W Film or Videotape The definition of a line integral; 27-0501 Purchase $205 Rental $21. distinguishing a line integral from a double integral; some examples; some general properties of line integrals; viewing the line integral as a definite integral. 24-min. B&W Film or Videotape 27-0504 Purchase $165 Rental $20.

MULTIPLE INTEGRATION- Complete. Set

Films/Videotapes Study Guide Complete set of five B&W Pretest, chalkboard photographs, 16 mm films or videotapes reading assignments, problems, 27-1500 Purchase $945 (SAVE $80) solutions, quiz. 290 pp. (One 25 Day Rental $99 (SAVE $10) per student recommended.) 27-2500 Purchase $9.50 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, A Complete Self-Study Subejct. Addison-Wesley, 1968, 818pp. The set offilms/videotapeo described above can be used as a complete self- 26-3000 Purchase $16.95 each. study subject when accompanied by the Study Guide, Suggested Text, and Supplementary Notes Supplementary Notes. A supplement to the text intro- ducing the concept of mathematical structure and expandingon dif- ficult topics in Calculus of Several Variables. 182 pp. 27-4000 Purchase $5.00 each.

18 19 Green's Theorem , Functions of a Complex Variable A discussion of simply-connected Rules which assign complex numbers regions; the statement of Green's to other complex numbers; a Theorem; an outline of the proof; geometric interpretation; an some comments about the theorem analytic and graphical introduc- showing how line integrals may tion to limits; derivatives of be related to multiple integrals; complex functions; Laplace's some examples; applying Green's equation. Theorem to regions which are 35-min. B&W Film or Videotape not simply-connected. 28-0102 Purchase $230 Rental $23. 40-min. B&W Film or Videotape 27-0505 Purchase $260 Rental $26. Conformal Mappings Review of mappings of the xy- plane into the uv-plane; the Complex Variables definition of a conformal map- ping; applications; conformal Five BMW 16mm mapping in the study of Laplace's Films or Videotapes equation; boundary value The Complex Numbers problems. Development of the real numbers; 36-min. B&W Film or Videotape complex numbers as a natural 28-0103 Purchase $235 Rental$24. outgrowth of the real numbers; arithmetical structure; polar coordinates and complex numbers; Sequences and Series applications; DeMoivre's Theorem; The concept of sequences and extracting the nth roots of a series applied to complex number. numbers; a pictorial interpreta- tion; defining sin z, log z, etc. 43-min. B&W Film or Videotape in terms of convergent power 28-0101 Purchase $275 Rental $28. series; application to series of real numbers;interva1 of convergence. 33-min. B&W Film or Videotape 28-0104 Purchase $220 Rental $22.

COMPLEX VARIABLES - Complete Set Films/Videotapes Study Guide Complete set of five B&W Pretest, chalkboard photographs 16 mm films or videotapes reading assignments, problems, solutions, quiz. 370 pp. 28-1100 Purchase $1090 (SAVE $95) (One per student recommended.) 25 Day Rental $110 (SAVE $10) 28-2100 Purchase $12.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, A Complete Self -Study Subject. Addison-Wesley, 1968, 818 pp. The set of filatelvideotapes described above can be used as a complete self - 26-3000 Purchase $16.95 each. study subject Ohm accompanied by the Study Guide, Suggested Text, and Supplementary Notes SiOlgewentar0 !Votes. A supplement to the text, providing background information on number systems and expanding on the concepts of linear inde- pendence and differential operators. 92 pp. 28-4000 Purchase $4.00 each.

19 20 COMPLEX VARIABLES - Continued.

Integrating Complex Functions Linear Differential Equations A review of the definite integral; Examples of non-linear differential extending the results to the equations; the definition of a case of complex numbers; line linear differential equation; integrals; integrating analytic some examples; properties of functions; integrals along linear equations; finding the closed curves. general solution of a linear 34-min. B&W Film or Videotape differential equation. 28-0105 Purchase $225 Rental $23. 35-min. B&W Film or Videotape 28-0202 Purchase $230 Rental $23. Differential Equations Solving the Linear Equation Seven B&W 16mm L(y) = 0; Constant Coefficients Films or Videotapes Trying for solutions in the form

The Concept of a General Solution y = er ; the problems involved Given f(x,y,y') does the equation with r being a non-real number; have a solution and if so is the the general concept of the solution unique? Some examples. reduced or homogeneous equation; Clairaut's Equation. The what happens if r is a repeated definition of a general solution. root of the auxiliary equation; Application to certain first some examples. degree differential equations. 19-min, B&W Film or Videotape More on exact differentials. 28-0203 Purchase $130 Rental $20. 34-min. B&W Film or Videotape 28-0201 Purchase $225 Rental $23.

DIFFERENTIAL EQUATIONS- Complete Set

Films/Videotapes Study Guide Complete set of seven B&W Pretest, chalkboard photographs 16 mm films or videotapes reading assignments, problems, 28-1200 Purchase $1300 (SAVE $115) solutions, quiz. 458 pp. 35 Day Rental $143 (SAVE $10) (One per student recommended.) 28-2200 Purchase $15.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, ACoarptete SeZP.Study Subject. Addison-Wesley, 1968, 818pp. The set offilms/Videotapes described above can be used as a oomplete self- 26-3000 Purchase $16.95 each study subject when accompanied by the Study Guide, Suggested Text,- and Supplementary Notes A4ppiementary Notes. A supplement to the text, providing background information on, number systems and expanding on'the concepts of linear inde- pendence and differential operators. 92 pp. 28-.4000 Purchase $4.00 each.

20 Undetermined Coefficients Laplace Transforms Find a solution of L(y) = f(x) Functions of exponential order; in the special case that the the definition of the Laplace coefficients are still constants transform of a function; computing and f(x) is either a polynomial, the Laplace transform of some an exponential function, or a special functions; some notes on function of the form sin mx or. Laplace transforms; the linear cos mx. The meaning of un- aspects of Laplace transforms; determined coefficients; the role a key property about Laplace of the reduced equation; the transforms; applications to method of guessing a trial linear differential equations; solution. Some applications. Lerch's Theorem. 29-min. B&W Film or Videotape 38-min. B&W Film or Videotape 28-0204 Purchase $195 Rental $20. 28-0207 Purchase $250 Rental $25.

Variation of Parameters A method for handling L(y) = f(x) Linear Algebia for any linear equation and more general categories for f(x); the Eight Ballemm derivation of the technique; how Films or Videotapes the technique is used; some Vector Spaces examples; a discussion of why An axiomatic definition of this technique is so valuable. structure; some important theorems; discussion of how the 24-min. B&W Film or Videotape axiomatic definition generalizes 28-0205 Purchase $165 Rental $20. the n-tuple definition; a geometric interpretation; the concept of a subspace. Power Series Solutions A review of previous techniques; 31-min. B&W Film or Videotape a key existence theorem; using 28-0301 Purchase $210 Rental $21. power series to find an existing solution; some examples. 33-min. B&W Film or Videotape 28-0206 Purchase $220 Rental $22.

LINEAR ALGEBRA - Complete Set Films/Videotapes Study Guide Complete set of eight B&W Pretest, chalkboard, photographs 16 mm films or videotapes reading assignments, problems, solutions, quiz. 398 pp. 28-1300 Purchase $1670 (SAVE $145) (One per student recommended.) 40 Day Rental $176 (SAVE $10) 28-2300 Purchase $13.00 each. Suggested Text (10% Discount on five or more.) Calculus and Analytic Geometry (Fourth Edition) by G.B. Thomas, A Complete Self -Study Subject. Addison-Wesley, 1968, 818 pp. The set of films /videotapes described above can be used as a complete self- 26-3000 Purchase $16.95 each. study subject when accompanied by the Study Guide, Suggested Text, and Supplementary Notes Supplementary Notes. A supplement to the text, providing background information on number systems and expanding on the concepts of linear inde- pendence and differential operators. 92 pp. 28-4000 Purchase $4.00 each.

21 22 LINEAR ALGEBRA - Continued

Spanning Vectors Eigenvectors Definition of spanningvectors; Solving the vector equation some examples; the definition of f(v) = cv; geometric interpreta- linear dependence and linearin- tion; some applications; a matrix dependence; some examples;a new approach to eigenvectors from look at the dimension ofa vector the choice of a basis; some space; constructive examples. important invariants; some 27-min. B&W Film or Videotape examples. 28-0302 Purchase $180Rental $20. 31-min. B&W Film or Videotape 28-0306 Purchase $210 Rental $21. Constructing Bases Review of previous lecture; Dot Products definition of a basis for a vector Generalized properties of the space; some important observations; dot product; examples; the constructing a basis for a given Gram-Schmidt orthogonalization vector space; the invariance of process; constructing an ortho- the dimension of a vector space normal basis for a given vector in terms of basis vectors; using space. matrices to show when one vector is a linear combination of other 41-min. B&W Film or Videotape vectors. 28-0307 Purchase $265 Rental $27. 36-min. B&W Film or Videotape 28-0303 Purchase $235 Rental $24. Orthogonal Functions Orthogonal functions; definition of Fourier series; some special Linear Transformations cases; constructing the Fourier Definition of a linear trans- series for some given functions formation; properties of linear and a pictorial interpretation; transformations; some examples; a discussion of errors. the relationship between linear transformations and matrices; 34-min. B&W Film or Videotape more examples; the matrix of a 28-0308 Purchase $225 Rental $23. linear transformation relative to a particular basis. 36-min. B&W Film or Videotape 28-0304 Purchase $235 Rental $24.

Determinants Inventing a technique for telling us when n vectors can be the basis of an n-dimensional vector space. The properties which define a determinant; some consequences of these properties; some examples and "short-cuts". 39-min. B&W Film or Videotape 28-0305 Purchase $255 Rental $26.

22 23 Colloid and Surface Chemistry J. Th. G. Overbeek

Colloid and Surface Chemistry our daily lives. An understanding is a set of 55 lectures and of electrokinetic phenomena has demonstrations on surface contributed to a number of chemistry, lyophobic colloids, analytical techniques and indus- electrokinetics and membrane trial processes. And lyophilic phenomena, and lyophilic colloids. colloids not only include the extremely important polymers and Interfacial phenomena play a reversible associates, but cons- significant role in a large number titute the very basis for life of processes in the chemical, in the form of proteins and petroleum, and metallurgical nucleic acids. industries as well as in the biological processes of life iteself. Lyophobic colloids -- J. Th. G. Overbeek is Professor paints, dyes, coatings, cosmetics, of Physical Chemistry at the pharmaceuticals, food products -- University of Utrecht in the also play an important role in Netherlands.

2.4 Colloid and Surface Chemistry Adsorption, Analytical Aspect Surface Chemistry Surface or interface is a region Sixteen B&W 16mm of finite thickness. Description of (positive or negative) surface Films or Videotapes excess with Gibbs dividing sur- Introduction to Colloid Chemistry face. Guggenheim method with and its Relation to Surface two dividing surfaces. Invariant Chemistry and Electrochemistry linear combinations of surface Disperse systems are of interest excesses. both for their many applications 25-min. B&W Film or Videotape and as systems worthy of fun- 11-0105 Purchase $170 Rental $20. damental study. Their large inter- facial area explains why surface chemistry and surface electro- Thermodynamics of Fluid Interfaces chemistry are intrinsic facets of The Gibbs adsorption equation colloid chemistry. and the concept of the surface 36-min. B&W Film or Videotape excess concentration. Importance 11-0101 Purchase $235 Rental $24. of -log c or-log a plots. Saturation adsorption. Critical micelle concentration. Surface Tension and Surface 48-min. B&W Film or Videotape Energies 11-0106 Purchase $305 Rental $31 Surface tension results from an inbalance of intermolecular forces. Relations between surface Spreading - Surface Films of tension and (Helmholtz and Gibbs) Insoluble Monolayers surface free energies. Hydrostatic Spreading tension, initial and pressure (Young, Laplace) and final. Neumann's triangle. modified vapor pressure (Kelvin) Influence of surfactants on at curved interfaces. spreading. Surface pressure. 40-min. B&W Film or Videotape Langmuir trough, film balance. 11-0102 Purchase260 Rental $26. Surface equation of state, surface potential, surface viscosity and elasticity. Effect of monolayers Measurement of Surface and on evaporation. Multilayers. Interfacial Tensions of 51-min. B&W Film or Videotape Liquids (1) 11-0107 Purchase $360 Rental $36. Static and dynamic measurements related to curvature of a meniscus: capillary rise or depression, maximum bubble pres- Surface Tension and Surface Structure of Solids sure, stalagmometer (drop weight). Experiments on surface tension. 25-min. B&W Film or Videotape Calculation of surface (free) 11-0103 Purchase $175 Rental $18. energies. Methods of determining .surface structure and modern spectroscopy and electronic Measurement of Surface and analytical methods. How to Interfacial Tensions of obtain large specific surface area. Liquids (2) 52-min. B&W Film or Videotape Sessile or pendant drop or bubble, 11-0108 Purchase $325 Rental $33. Wilhelmi plate, du Nouy ring, surface ripples, oscillating jet. 37-min. B&W Film or Videotape 11-0104 Purchase$260 Rental $26.

24 25 Adsorption of Gases on Solids Energies and Entropy of Adsorption Physisorption, chemisorption. Relations between r, Tr (or y) and Adsorption isotherms, Langmuir, c (or p). Calorimetric and BET, Harkins and Jura, Polanyi, isosteric heats of adsorption. Frenkel, Halsey, Hill, de Boer Enthalpies and entropies in (t-plot). Heterogeneity. Steps models, such as Langmuir, B.E.T., in isotherms. Capillary mobile monolayer. Conversion of condensation, hysteresis, pore adsorption isotherm into equation size distribution. of state and vice versa. 54-min. B&W Film or Videotape 41-min. B&W Film or Videotape 11-0109 Purchase $330 Rental $33. 11-0112 Purchase $265 Rental $27.

Chemisorption - Adsorption from Charged Interfaces - Electro- Solution chemistry of the Phase Boundary Chemisorption, monolayer, large Lippmann equation. Electro- heat of adsorption, Freundlich neutrality of interfaces. (Kuster) isotherm. Adsorption Completely reversible and com- from solution is always competi- pletely polarizable electrodes. tive. Determination of adsorption. Potential determining ions. Traube's rule (standard free 39-min. B&W Film or Videotape energy of adsorption per CH2-group. 11-0113 Purchase $255 Rental $26. 30-min. B&W Film or Videotape 11-0110 Purchase $210 Rental $21. Surface Potentials - Structure of the Electric Double Layer Outer and inner electric poten- Adsorption from Solution, tial difference. "Real potential." Continued. Contact Angles Double layer. Poisson-Boltzmann Adsorption of polymers, of ions. equation. Gouy, Chapman, Stern Negative adsorption. Chromato- models. Thickness and capacity graphy. Contact angle. Influence of double layer. of surfactants. Wetting, dewet- ting, froth-flotation. Contact 54-min. B&W Film or Videotape angle hysteresis. 11-0114 Purchase $380 Rental $38. 42-min. B&W Film or Videotape 11-0111 Purchase $295 Rental $30.

SURFACE CHEMISTRY - Complete Set Study Guide Films/Videotapes Lecture summaries and discus- Complete set of sixteen B&W sions, photographs, reading 16 mm films or videotapes. assignments, problems, and 11-1100 Purchase $3900 (SAVE $580) problem solutions. 278 pp. 80 Day Rental $410 (SAVE $45) (One per student recommended.) 11-2100 Purchase $12.00 each. Suggested Text (10% Discount on five or more.) Physical Chemistry of Surfaces by A.W. Adamson, Interscience, A Complete Self-Study Subject. (Second Edition), 1967, 747 pp. The set of films/videotapes described 11-3100 Purchase $21.75 each. above can he used as a complete self- study subject when accompanied by the Study Guide and Suggested Text.

25 26 SURFACE CHEMISTRY - Continued

A Few Special Aspects of Double Interaction Between Spherical Layers Double Layers - Schiller Layers Negative adsorption of co-ions. and Other Experiments on Double Ion-exchange. Point of zero Layer Interaction charge. Double layers in ionic Derjaguin's method for spheres... crystals and semiconductors. small separations...large Rate of charge adjustment. separations...Schiller layers, 42-min. B&W Film or Videotape Tobacco mosaic virus, lipid layers. 11-0115 Purchase $270 Rental $27. 36-min. B&W Film or Videotape 11-0203 Purchase $250 Rental $25. Free Energy of Double Layers - Electrocapillarity Van der Waals Forces Calculation of surface free Van der Waals forces responsible r energy: Chemical and electrical for long range attraction... parts. Electrocapillary curve. additivity...flat plates, 'Charge and capacitance for spheres. Hg /aqueous solutions. Other double layers: inorganics, oil, 29-min. B&W Film or Videotape and-gas, all against water. 11-0204 Purchase $195 Rental $20. 55 min. B&W Film or Videotape 11-0116 Purchase $385 Rental $39. Van der Waals Forces - Influence of a Medium - Retardation- Lifshitz Method - Experiments Van der Waals forces between Lyophobic Colloids particles in a medium always attractive...retardation at Fifteen B&W 16mm large distances...Lifshitz' Films or Videotapes approach...experiments. Introduction on Stability of Lyophobic Colloids 39-min B&W Film or Videotape 11-0205 Purchase $255,Rental $26. Size Range (lnm 1Pm) of col- loidal particles...distinction between lyophobic and lyophilic coldoids...emphasis on stability Combinations of Attraction and,,,. and coagulation (= flocculation) Repulsion - Application to of lyophobic colloids and other Colloid Stability geometries. Potential energy curves...rule of Schulze and Hardy...flocculation 29-min. B&W Film or Videotape series...DLVO theory...ions with 11-0201 Purchase $195 Rental $20. abnormal flocculating power... irregular series...charge reversal. Interaction Between Two Double 38-min. B&W Film or Videotape Layers 11-0206 Purchase $270 Rental $27. Two parallel flat double layers... Poisson-Boltzmann equation... constant charge or constant Colloid Stability - Lyotropic Effects - Repeptization surface potential...change in Gibbs free energy...Langmuir's Influence of lyotropic series on force method...Stern correction. flocculation...requirements for reversibility (repeptization)... 47-min. B&W Film or Videotape secondary minimum...mutual 11-0202 Purchase $330 Rental $33. flocculation. 40-min. B&W Film or Videotape 11-0207 Purchase $280 Rental $28.

26 2`7 Foams and Soap Films (1) Steric Stabilization - Sensitized Coarsening of foams by diffusion, Flocculation drainage, and breaking...color Stabilization by adsorbed polymers and thickness of soap films...... anchor and tail (or loop)... black soap films...self-healing repulsion by osmotic effect and Gibbs-Marangoni effect... by restriction of possible con- drainage mechanisms...Van der formations...examples...sensitized Waals and repulsive forces. flocculation due to bridging... applications. 39-min. B&W Film or Videotape 11-0208 Purchase $275 Rental $28. 41-min. B&W Film or Videotape 11-0211 Purchase $290 Rental $29

Foams and Soap Films (2) Second black films...foam Coarse Suspensions - Rheology breakers...light scattering and Sediment density and flow behavior breaking due to surface fluctua- as funciton of suspension tions...sharp transition of stability...thixotropy...gel colored (silver) to black formation by flocculation or films...applications of foams. addition of third phase... applications. 38-min. B&W Film or Videotape 11-0209 Purchase $270 Rental $27. 57-min. B&W Film or Videotape 11-0212 Purchase $395 Rental $39.

Emulsions - Suspensions in Non-Aqueous Media Sol Preparation, Dialysis and Emulsions stabilized by surfactants Ultrafiltration or by finely divided solids... Dispersion and condensation creaming, coalescence, breaking... methods...preparing isodisperse 0/W and W/0 emulsions...inversion sols...dialysis, electrodialysis, ...applications of emulsions... ultrafiltration...demonstration non-aqueous suspensions: stabi- of preparation of several sols... lity, as affected by electrolytes, spontaneous emulsification. permitivity, and particle concentration...applica- 57-min. B&W Film or Videotape 11-0213 Purchase $395 Rental $39. tions. 39-min. B&W Film or Videotape 11-0210 Purchase $275 Rental $28.

LYOPHOBIC COLLOIDS - Complete Set

Films/Videotapes Study Guide Complete set offifteenB&W Lecture. sUmmarle4 and 16 mm films or videotapes. Slone, photographer reading eissignmentS, PrObiemer and 11-1200 Purchase $3840 (SAVE $575) 75 Day Rental $399-(SAVE $44) Problem solutions: 302 PP. (One per student recommended.) Suggested Texts 11-2200 Purchase $13.00 each. Physical Chemistry of Surfaces by (10% OlScount on five or more-) A.W. AdaMson, Interscience, A ampieteSW414M44, Subject. (Second Edition), 1967, 747 pP. The set of fitixtivid±201,Wee described 11-3100 Purchase $21.75 each. above can be401414air -GoVieteOaf- etudY eubjact when awartkorted by Colloid Science Volume 1 edited the Study Cade and gaggeeted Text. by H. R. Kruyt, Elsevier Publish- ing COmpany, 1974, 389 pp. 11.-3200 Purchase $24C0t each

27 28 LYOPHOBIC COLLOIDS - Continued

Particle Size Determination - Applications of Electrokinetics Optics Influence of counterion charge Microscope...sedimentation... and concentration on zeta-potential Coulter counter...electron- ...Concept of "slipping plane"... microscope...ultramicroscope... Techniques for determining Tyndall light...Rayleigh and Mie electrophoretic mobility and for theories...higher order Tyndall preparative electrophoresis... spectra...birefringence... Applications, including fire tactoids. hazards of high streaming poten- 56-min. B&W Film or Videotape tials, separation of protein 11-0214 Purchase $395 Rental $39. mixture, concentrating sols by electrodecantation, electro- deposition of latex and pigments Kinetics of Flocculation from suspensions. Rapid and slow flocculation... 53-min. B&W Film or Videotape Von Smoluchowski's theory... 11-0303 Purchase $370 Rental $37. extension by Fuchs to slow floc- culation...log W - log c curves ...experiments...influence of stirring. Non-Equilibrium Thermodynamics 57-min. B&W Film or Videotape Applied to Electroosmosis and 11-0215 Purchase $345 Rental $35. Streaming Potential Entropy production in irreversi- ble phenomena...Fluctuations... Onsager's reciprocal relations Electrokinetics and ..Saxen's relation between Membrane Phenomena electroosmosis and streaming potential. , Nine B&W 16mm 38-min. B&W Film or Videotape Films or Videotapes 11-0304 Purchase $250 Rental $25. Introduction. The Four Electrokinetic Effects. The Zeta-Potential Schmid Membrane Model. Non- Relationships between liquid Equilibrium Thermodynamics of motion and electric field near Electrophoresis and Sedimentation an interface...Electroosmosis, Potential electrophoresis, electrodeposition, In Schmid model for membrane streaming potential, streaming is replaced by density of fixed current, migration potential. charges...Electrophoresis and sedimentation potential con- 54-min. B&W Film or Videotape nected by Onsager relation... 11-0301 Purchase $380 Rental $38. Concentration dependence of rate of sedimentation. Theory of Electrophoresis 30-min. B&W Film or Videotape Influence of Ka (K = reciprocal 11-0305 Purchase $205 Rental $21. thickness of double layer, a = radius of particle) on electro- phoretic mobility.. Relaxation Introduction to Membrane effects. Potentials Treatment based on galvanic 29-min. B&W Film or Videotape cell reaction...Reversible 11-0302 Purchase $195 Rental $20. - electrodes or salt bridges. 26-min. B&W Film or Videotape 11-0306 Purchase $175 Rental $20

28 29 Membrane Potentials. Incomplete Selectivity; B3 -Ionic Potentials; Lyophilic Colloids Filtration through Membrane Fifteen B&W 16mm Selectivity based on fixed Films or Videotapes charge of the membrane...Meyer- Sievers - Theorell theory of it Introduction. Solutions of complete selectivity...Bi-ionic Lyophilic Colloids. Examples potentials...Desalination by of Macromolecules electrodialysis...Flow of ions, Solutions of polymers...Survey solvent, electric current of biocolloids, synthetic poly- through membrane. mers and polycondensates, their role in nature and fields of 40-min. B&W Film or Videotape application. 11-0307 Purchase $260 Rental $26. 55-min. B&W Film or Videotape 11-0401 Purchase $385 Rental $39. The Donnan Equilibrium Donnan treatment of distri- bution of ions, osmotic Polymer Synthesis. The Impor- pressure and membrane potential tance of Polymers. Their Spe- ...Non-ideality based on cific Role inhomogeneity of Donnan phase. Free radical polymerization. Kinetic aspects. Pearl-and 39-min. B&W Film or Videotape emulsion-polymerization. Ionic 11-0308 Purchase $255 Rental $25. polymerization. Stereo-regular polymers. Polycondensation. Intra - and intermolecular The Donnan Potential. The forces, rubber elasticity, in- Suspension Effect formation storage in biopolymers. Donnan potential treated as a series of three diffusion 55-min. B&W Film or Videotape potentials...Importance of con- 11-0402 Purchase $385 Rental$39. tributions of liquid junctions with saturated KC1..The suspension (Wiegner-Pallmann) Statistics of Polymer Coil Con- effect. formations. Viscosity of Poly- 30-min. B&W Film or Videotape mer Solutions 11-0309 Purchase $205 Rental $21. Random flight statistics. Dis- tribution function of end-to- end distance. "Statistical chain element." Viscosity of solutions of coils.

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ELECTROK/NETICS - Complete Set. Study Guide Films/Videotapes Lecture summaries and discus- Complete set of nine B&W sions, photographs, reading 16 mm films or videotapes. assignments, problems,.and problem solutions. 156 pP 11-1300 Purchase $2065 (SAVE $230) (One per student recoMMended.) 45 Day Rental $217 (SAVE $16)' 11-2300 Purchase $6.50 each Suggested Text (10% Discount on five or more.) Colloid Science Volume 1 Edited AComplAte0BWIf-Sti4 by H.R. Rruyt, Elsevier Publish- The set of described ing Company, 1574, 389 pp. above can be used ae aompiete self- 11-3200 Purchase $26.00. etudya:44feet when, asevevanied by Me Study Guide and Suggested Text.

30 29 LYOPHILIC COLLOI - continued

Rubber Elasticity. Light Scattering Force vs. elongation relation Light Scattering in Rayleigh for ideal rubber derived from approximation (size

Thermodynamics of Polymer Solu- The Ultracentrifuge tions. Osmotic Pressure Rate of sedimentation and diffu- Flory-Huggins theory. Quasi- sion. The Svedberg equation. lattice model. Energy, entropy Shape factor. Sedimentation and free energy of mixing "Very equilibrium. Archibald method. dilute" solutions. Theta-tem- Applications. perature. Fractionation. 51-min. B&W Film or Videotape 52-min. B&W Film or Videotape 11-0408 Purchase $320 Rental $32. 11-0405 Purchase $325 Rental $33.

Polyelectrolytes. Examples, Molecular Weight Distributions. Titration Curves, Electrophoresis Determination of Average Molecu- Examples of natural and synthetic lar Weight by Osmotic Pressure, polyelectrolytes. Titration Chemical Analysis, Viscosity curve gives information on elec- Integral. (or cumulative) and trical free energy of coil. Ti- differential molecular weight tration of proteins. Iso-electric distributions. Different kinds point. of average molecular weights. Number average M. Viscosity 38-min. B&W Film or Videotape average M. 11-0409 Purchase $250 Rental $25. 42-min. B&W Film or Videotape 11-0406 Purchase $270 Rental $27.

LYOPHILIC COLLOIDS - Complete Set Films/Videotapes Study Guide Complete set of fifteen B&W Lecture summaries and.Oiscus- 16 pm films or videotapes. sions, ptotographs, 11-1400 Purchase $4125 (SAVE $615) assignments, Problems, and problem solutions. 306 PP- 75 Day Rental $430 (SAVE $48> (One per student recommended.) SuggeSted Text 11-2400 Purchime $13.00 each. (10% Discount on five or more.) Principles, of. Polymer Chemistry by Paul J. Flory, Cornell University A ampieteStaf-Study, Subject. Press, 1971, 672 pp. The eetof fibmioideotaPes Oummibed 11..3400 Purchase $24.50 each. atom otm be mod as a catelete sett- study subjeat when addlatrented the StudyGuideand SefigeetedText.

30 31 Polyelectrolytes. Viscosity, Association Colloids. Micelle Light Scattering, Osmotic Pressure, Formation. Phase Diagrams Sedimentation Critical micelle concentration. Three causes for the electro- Size and shape of micelles. Law viscous effect are expansion of of mass-action explains sharp coils, deformation of double c.m.c. Driving force for micelle layer and mutual repulsion of formation mostly entropy based. polyions. Light scattering de- Influence of salt concentration pends strongly on 0 and c. of c.m.c. and micelle size. 49-min. B&W Film or Videotape 55-min. B&W Film or Videotape 11-0410 Purchase $310 Rental $31. 11-0413 Purchase $335 Rental $34.

Coacervation, Salting Out Association Colloids. Micellar Precipitation of polyelectro- Size. Thermodynamics. Applica- lytes by organic non-solvents tions and electrolytes..."Salting out" Micelle molecular weight ...Lyotropic series...Properties best by light scattering. Cor- of coacervates. Complexcoacer- rection for negative adsorption vates between polycations and of co-ions. Thermodynamics of polyanions...Double Schulze- micelle formation. Hartley, Hardy rule. Incompatibility of Debye, Stigter. Cell membrane. non-charged polymers. Nucleo- proteins and globulins. 50-min. B&W Film or Videotape 11-0414 Purchase $315 Rental $32. 49-min. B&W Film or Videotape 11-0411 Purchase $345 Rental $35. Gels Structural requirements for gel- Complexcoacervates. ation. Sharp gel point. Crystal- Electrophoresis. Structure of line regions as crosslinks. Proteins and Nucleic Acids Syneresis. Soap gels, jelly and Buchner-effect and decomposition curd. Swelling. "Memory" of in electrophoresis. Autocomplex- gels. Theory of swelling. Poly- coacervation. Theory of complex- electrolyte gels.Mechano- coacervation based on Flory- chemistry. Huggins theory with addition of electrostatic interaction. 48-min. B&W Film or Videotape Microencapsulation. Helical 11-0415 Purchase $335 Rental $34. structures in proteins and nucleic acids. Denaturation.

59-min.136,107 Film or Videotape 11-0412 Purchase $395 Rental $39.

A Visit with J. Th. G. Overbeek The serious lecturer of the Colloid and Surface Chemistry series gives way to the warm human being behind the: theories and demonstrations. In an in-' terview with John T. Fitch of the MIT Center for Advanced Engineer-. ing Study, Theo Overbeek recounts his life story (baginning with his "firm decision* not to be a teacher!) including the develop- ment of the D.L.V.O.theory. 30-min. Color Videotape 11-0501 Purchase $210 Rental $21.

32 31 Computer Languages Michael L. Dertouzos

Computer Languages: Structure and . the translation of a language Interpretation focuses on issues into the constructs of another which must be addressed in the language. design or implementation of any programming system -- independent The videotapes in this series of its individual details. These comprise un-edited lectures and issues include: classroom discussions as well as the means by which a variable is four specially prepared studio associated with its value. productions.

. the time at which the value of a variable is calculated. Michael L. Dertouzos is Professor the logical power of a language of Electrical Engineering and Computer Science at MIT and the efficiency and expressibility Director of the MIT Laboratory for of a language. Computer Science (formerly Project the use of functions to process MAC). other' functions.

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32 33 Computer Languages

Thirty -nine Assembly Language Color Videotapes Goals of assembly language. Structure of A(M): lables, Introduction to Computer Science mnemonics, address calculation; This lecture is a succinct answer Pseudo operations; symbolic expres- to two basic questions: sions. ASCII codes; the name- (1) What is computer Science? value distinction. (2) How does it differ, in its nature, from the other sciences Z50 -min. Color Videotape and engineering disciplines? 14-0106 Purchase $300 Rental $30. In answering these questions, the

lecture states the premises and . goals of the course, and outlines Structure of Assemblers the material that Will be covered. The translation process. How A(M) works; use of symbol tables. :50-min. Color Videotape 1 vs. 2 passes. Space-time trade- 14-0101 Purchase $300 Rental $30. offs. :50-min. Color Videotape Introduction to Machine Language 14-0107 Purchase $300 Rental $30. Early processor and memory access Need for relative addres- models. Applicative Expressions (AEs) sing, indirection, stacks, sub- Overview of M machine Applicative vs. imperative routines. features of languages. Informal (PDP-11) instruction set. Byte/ Universe of word addressing. Execution cycle. syntax of AEs. discourse. Informal semantics. :50-min. Color Videotape :50-min. Color Videotape 14-0102 Purchase $300 Rental $30. 14-0108 Purchase $3G0 Rental $30.

M Machine Language Meaning of AEs me Addressing modes, instruction Functionality. Development of formats. Types of instructions; the normal value algorithm from opcodes. Examples. Octal vs. intuitive notions of meaning. binary notation. The substitution rule. :50-min. Color Videotape :50-min. Color Videotape ld-0103 Purchase $30Q Rental $30. 14 -0109 Purchase $300 Rental $30.

The Need for Subroutines & Stacks Use of the Normal Value Algorithm. Backus-Naur Form (BNF) as a Evaluations using the nv algorithm. recursive structure definition. Free and bound variables. Condi- Use of a stack for implementing tionals, logic values. recursive programs. Examples. 2:50-min. Color Videotape :50-min. Color Videotape 14-0110 Purchase $300 Rental $30. 14-0104 Purchase $300 Rental $30.

Conditionals Subroutines and Stack Discipline Stack discipline Review of free & bound variables. Stack operations. Different ways of implementing and its importance. Mathematical Subroutines; types conditional operations. Impor- induction. tance of not evaluating both of call-return sequences. Methods The JSR branches. Augmentation of the of passing parameters. nv algorithm. and RTS instructions. :50-min. Color Videotape 50 -min. Color Videotape 14-0111 Purchase $300 Rental $30. 14-0105 Purchase $300 Rental $30.

3 4 33 COMPUTER LANGUAGES - Continued

Ramifications of Normal Value Logical Power of Computing Relativity of priviledged names. Schemes Implications of changes in order The theoretical notions of of evaluation. Church-Rosser computability and universality theorem explained intuitively. are the central issues of this Control trees. lecture. Topics covered "z50-min. Color Videotape ihclude: 14-0112 Purchase $300 Rental $30. Turing machines coding schemes proof that uncomputable functions exist Introduction to Environments Russell's paradox Motivation for binding variables universality - the Church-Turing to values in an environment. The thesis global environment; bind, lookup tests for universality functions. Definitrniiiof the global environment evaluator Z50-min. Color Videotape (G-machine). 14-0118 Purchase $300 Rental $30. Z50-min. Color Videotape 14-0113 Purchase $300 Rental $30. Recursive Function Theory This lecture continues the subject of computability that was begun Problems of the G-Machine in Lecture 14-0118 by defining the Review of G-machine algorithm. computing scheme known as the Control trees, recursion in the recursive functions. Examples G-machine. Demonstration of of recursive functions are identifier collision. constructed, and the importance z50-min. Color Videotape of the scheme is discussed. 14-0114 Purchase $300 Rental $30. (Recursive function theory should not be confused with recursive programming.) The Stack Environment (S-Machine) "z50-min. Color Videotape Identifier collision as motivation 14-0119 Purchase $300 Rental $30. for a stack structured environment. Definition of the S-machine. Control trees. Introduction to LISP 50-min. Color Videotape Pure LISP in relation to AEs. 14-0115 Purchase $300 Rental $30. Arithmetic functions and predicates. COND syntax. The LABEL primitive. Z50-min. Color Videotape Recursion in G & S 14-0120 Purchase $300 Rental $30. Examples demonstrating the implementation of recursive programs in global and stack S-Expressions environments. (Quiz review,) S-expressions and the functions Z50-min. Color Videotape which operate on them. CAR, CDR, 14-0116 Purchase $300 Rental $30. CONS. List notation. :=60-min. Color Videotape 14-0121 Purchase $300 Rental $30. Abstract Recursion The advantages of recursion over iteration. Recursive programs in Lists normal order. The fixed point Lists and atoms. The pseudo- property; the Y operator. function QUOTE and its significance. Examples. Programming techniques for list Z50-min. Color Videotape processing functions. 14-0117 Purchase $300 Rental $30. Z50-min. Color Videotape 14-0122 Purchase $300 Rental $30.

34 35 Evaluators (1) Tree Environment (2) Development of the S-machine Upward funarg problem, as eval- (stack evaluator for AEs) written uated by the T-machine. Sketch in LISP. of equivalence proof for tree machine and normal order algorithm. Z50-min. Color Videotape 14-0123 Purchase $300 Rental $30. 250-min. Color Videotape 14-0130 Purchase $300 Rental $30.

Evaluators (2) Conclusion of S-machine in LISP. Imperative LISP (1) Minimal pure LISP evaluator Syntax and semantics of SET, SETQ; written in LISP. DEFUN; motivation for and usage of, RPLACA, RPLACD. Z50-min. Color Videotape 14-0124 Purchase $300 Rental $30. Z50-min. Color Videotape 14-0131 Purchase $300 Rental $30.

Evaluators (3) The classic EVAL-APPLY structured Imperative LISP (2) LISP evaluator, in LISP. Extensi- Review RPLACA, RPLACD. Construc- bility of the model. Why QUOTE tion of circular lists. Imple- is not a function. mentation of SET and SETQ. Call by name; call by value. Call 7:50-min. Color Videotape by reference. 14-0125 Purchase $300 Rental $30. Z50-min. Color Videotape 14-0132 Purchase $300 Rental $30. Evaluators (4) Comparison of MPLEVAL, EVAL-APPLY, Sequencing and normal order schemes. Levels The primitives PROG2, PROGN. of evaluation. Implementation of The PROG construct; RETURN, GO, lists. Box-pointer notation; labels. Motivate global labels sharing. (label closures). Z50-min. Color Videotape Z50-min. Color Videotape 14-0126 Purchase $300 Rental $30. 14-0133 Purchase $300 Rental $30.

FUNARG Problems (SAW) Dynamic Allocation of Storage Peculiarities of DELPHI LISP. The free storage list. Garbage Upward and downward FUNARG func- collection - marking and sweeping. tional argument) problems as a Reference counters. The Deutsch consequence of a stack-structured algorithm. environment. Motivation of tree structuredenvironment. Z50-min. Color Videotape 14-0134 Purchase $300 Rental $30. Z50-min. Color Videotape 14-0127 Purchase $300 Rental $30. Global Labels (1) The control state. Problems Possible Cures for FUNARG Problems caused by non-local GOs. Informal usage of function Development of label closures as closures (T-machine). Control solution. trees in the T-machine. Z50-min. Color Videotape Z50-min. Color Videotape 14-0135 Purchase $300 Rental $30. 14-0128 Purchase $300 Rental $30.

Global Labels (2) Tree Environment (1) Application of global labels in Definition of T-machine in LISP, error handling, backtracking. as a modificationof the Multiprocessing using label S-machine. Examples of usage. closures. Z50-min. Color Videotape Z50-min. Color Videotape 14-0129 Purchase $300 Rental$30. 14-0136 Purchase $300 Rental $30.

35 COMPUTER LANGUAGES Continued

Principles of Translation Machine Language Relation of translation to Covers the material of 14-0102 and interpretation. Efficiency 14-0103 in compressed form. Uses advantages of translation. the PDP-11 as an example of an Translation of AE's to LISP. actual machine. Topics include Z50-min. Color Videotape organization of the machine and 14-0137 Purchase $300 Rental $30. its major components, the various representations of data, the execution cycle of the machine, AE's to Assembly Language (1) and the actions performed by a Overall plan - applicative to sampling of the machine's instruc- imperative schemes. Translation tion repertoire: time environments. Shallow 55-min. Color Videotape binding. Need for run-time 14-0201 Purchase $385 Rental $39. interpretation. 7...:50-min. Color Videotape 14-0138 Purchase $300 Rental $30. Assembly Language, Subroutines, and Stacks Covers the material of 14-0104, AE's to Assembly Language (2) 14-0105, and 14-0106 in compres- Continuation of previous recitation with an example sed form. Includes symbolic labels and expressions, mnemonics, worked out. pseudooperations, subroutines. Z50-min. Color Videotape Motivates stacks as a means for 14-0139 Purchase $300 Rental $30. storing subroutine return points. Develops notion of stack discipline. 55-min. Color Videotape COMPUTER LANGUAGES - Complete Set 14-0202 Purchase $385 Rental $39. Color Videotapes Complete set of thirty-nine Recursion Color Videotapes Visiting Professor Joseph Stoy 14-1100 Purchase $9945 (SAVE $1755) explains and demonstrates the 195 Day Rental $995 (SAVE $175) process of writing recursive programs, i.e. programs that invoke themselves. Detailed examples are illustrated (viz. three "monks" working on the Towers of Hanoi puzzle) and worked out to. clarify this frequently misunderstood topic. 40-min. Color Videotape 14-0203 Purchase $330 Rental $33.

The following four videotapes are DELPHI color studio productions. The A demonstration of the.DELPHI first two cover some of the timesharing system at material in the classroom lectures a level designed for the studentwith a and recitations listed above in minimum of previous compressed form. They can be computer experience. Instruction includes: used in place of the earlier tapes logging in and out, using for students with more programming the editor and assembler,and using experience. The second two tapes the LISP interpreter. augment the lectures and recita- tions and can usefully be shown 49-min. Color Videotape in conjunction with them. 14-0204 'Purchase $370Rental $37.

36 3 7 Digital Signal Processing Alan V. Oppenheim

Digital Signal Processing is now This series of lectures and demon- being applied to such diverse strations begins with the defini- areas as biomedical engineering, tion of discrete time signals and acoustics, sonar, radar, seismology, systems. Topics covered include speech communication, telephony, difference equations, discrete nuclear science, and image proces- time Fourier transforms, the sing. This widespread application z-transform, digital filter has been due, in large part, to design and implementation, and the advances in integrated circuit the fast Fourier transform. technology which have had a pro- found impact on the techniques for transmitting and processing Alan V. Oppenheim is Associate electrical signals. Professor of Electrical Engineering and Computer Science at MIT.

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Twenty-one Sampling, Aliasing, and Frequency Color Videotapes Response Demonstration of sampling and Introduction aliasing with a sinusoidal signal. Provides an overview of the course Sinusoidal response of a digital and discusses some of the applica- filter. Dependence of frequency tions of digital signal proces- response on sampling period. sing. Periodic nature of the frequency response of a digital filter.. 17-min. Color Videotape 22-0101 Purchase $170 Rental $20. 30-min. Color Videotape 22-0121 Purchase $275 Rental $28.

Discrete-Time Signals and Systems (1) Demonstration of Sampling, Definition of basic discrete-time Aliasing, and Frequency Response signals: The unit sample, unit Demonstrations (only) from above. step, exponential and sinusoidal 12-min. Color Videotape sequences. Definitions and repre- 22-0122 Purchase $120 Rental $20. sentations of linear time- invariant discrete time systems. Properties of discrete-time The Z-Transform convolution. Relationship between the Fourier 36-min. Color Videotape transform and the z-transform. 22-0102 Purchase $310 Rental $31. Region of convergence for z- transforms. Relationship between region of convergence, causality Discrete-time Signals and and stability. Systems (2) 51-min. Color Videotape Stability and causality for 22-0105 Purchase $375 Rental $38. discrete-time systems. Systems describable by linear constant- coefficient difference equations. The Inverse Z- Transform Frequency response of linear Techniques for determining the time-invariant systems. inverse z-transform: inspection 50-min. Color Videotape method, use of power series expan- 22-0103 Purchase $375 Rental $38. sion, partial fraction expansion, use of contour integration. 46-min. Color Videotape The Discrete-Time Fourier Transform 22-0106 Purchase $360 Rental $36. Generalization of the frequency response representation of sequences. Inverse Fourier Z-Transform Properties transform relAtion. Properties Geometric determination of fre- between continous-time and quency response from pole-zero discrete-time Fourier transforms. patterns in the z-plane. Prop- 44-min. Color Videotape erties of z-transforms: scaling, 22-0104 Purchase $350 Rental $35. differentiation, shifting, convolution, etc. 56-min. Color Videotape 22-0107 Purchase $390 Rental $39.

38 33 The Discrete-Fourier Series Network Structures for Infinite Fourier series representation for Impulse Response (IIR) Digital periodic sequences. Determination Filters of Fourier series coefficients. Basic network structures for IIR Properties of Fourier Series. filters: direct cascade and parallel form. Canonic structures. 43-min. Color Videotape Transposition theorem for digital 22-0108 Purchase $345 Rental $35. networks and the resulting trans- posed forms. The Discrete-Fourier Transform 40-min. Color Videotape Fourier representation of finite 22-0112 Purchase $330 Rental $33. length sequences. Relationship between the Discrete-Fourier series. Properties of the Discrete- Network Structures for Finite Fourier transform: Symmetry, Impulse Response (FIR) Digital circular shifting, circular Filters and Parameter-Quantization convolution, etc. Effects in Digital Filter Structures 47-min. Color Videotape Direct form FIR filters. Efficient 22-0109 Purchase $360 Rental $36. implementation of FIR filters with linear phase. Frequency sampling Circular Convolution structure. Effects of parameter Circullar convolution of finite quantization in digital filter implementation. length sequences. Interpretation of circular convolution as linear 51-min. Color Videotape convolution followed by aliasing. 22-0113 Purchase $375 Rental $38. Implementing linear convolution by means of circular convolution. 43-min. Color Videotape Design of IIR Digital Filters (1) 22-0110 Purchase $345 Rental $35. Transformation of analog filter designs to digital filter designs; Approximation of derivatives by Representation of Linear Digital differences. Impulse invariant Networks design procedures. Block diagram representation of 07-min. Color Videotape difference equations. Linear 22-0114 Purchase $360 Rental $36. signal flow graphs. Flow graph representation of difference equations. Matrix representation of digital networks. Computability of digital networks. 52-min. Color Videotape 22-0111 Purchase $380 Rental $38.

DIGITAL SIGNAL PROCESSING - Complete Set

Color Videotapes Study Guide Complete set of twenty-one Chalkboard photographs, comments, Color Videotapes. reading assignments, problems, 22-1100 Purchase $6180 (SAVE $1020) and problem solutions. 260 pp. 105 Day Rental $646 (SAVE $82) (One per student recommended.) 22-2100 Purchase $11.00 each. Suggested Text (10% Discount on five or more.) Digital Signal Processing by A.V. Oppenheim and R. W. Schafer, A Complete Self-Study Subject. Prentice Hall, 1975, 585 pp. The set of videotapes described above can be used as a complete self- 22-3100 Purchase $21.95 each. study subject when accompanied by the Study Guide and Suggested Text.

39 do DIGITAL SIGNAL PROCESSING Continued

Design of IIR Digital Filters (2) Computation of the Discrete Digital filter design using the Fourier Transform (2) bilinear transformation. Frequency Interpretation of FFT flow graph warping introduced by the bilinear for in-place computation. Bit- transformation. Algorithmic design reversed data ordering. Other procedures for IIR filters. decimation-in-time FFT algorithms 41-min. Color Videotape by rearrangement of the flow- 22-0115 Purchase $335 Rental $34. graph. Decimation-in-frequency FFT algorithm. 44-min. Color Videotape Examples of IIR Filter Design 22-0119 Purchase $350 Rental $35. Design of digital Butterworth filter using impulse invariance. Design of digital Butterworth Computation of the Discrete filter using the bilinear trans- Fourier Transform (3) formation. Comparison of the Rearrangements of the basic resulting designs. decimation-in-frequency 48-min. Color Videotape algorithm. Relation between 22-0116 Purchase $365 Rental $37. decimation-in-time and decimation - in- frequency through the trans- position theorem. Arbitrary Design of FIR Digital Filters radix FFT algorithms. Design of FIR filters using 45-min. Color Videotape windows. Comparison of rectangular, 22-0120 Purchase $355 Rental $36. Bartlett and Hamming windows. Frequency sampling method of filter design. Optimum equiripple FIR filters. 39-min. Color Videotape

. 22-0117 Purchase $325 Rental $33.

Computation of the Discrete Fourier Transform (1) Direct computation of the discrete Fourier transform. Computation resulting from successive decimation of the sequences. The decimation- in-time form of the fast Fourier transform (FFT) algorithm. Basic butterfly computation. 49-min. Color Videotape 22-0118 Purchase $370 Rental $37.

40 41 Economics Robert S. Pindyck

Economics is a subject that regulation of particular indus- confronts us every day -- whether tries?Why do shortages of oil, we like it or not. National gasoline, or various foodstuffs politics, for example, are inter occur? These questions can twined with issues of economic better be understood by one who policy: Should the federal is familiar with the behavior budget contain a deficit or a of consumers, firms, and individual surplus and should the Federal markets. Reserve expand or contract the money supply? How can the No previous study of economics government deal with problems of is assumed, but a student with inflation and unemployment? These a working knowledge of differential are problems in macroeconomics. calculus will get the most out of this approach to the material. But, pick up a newspaper and you will be confronted with micro- economic issues as well. Should Robert S. Pindyck is Associate the government tighten its Professor of Management at MIT.

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42 Economics

Microeconomics Market Supply and Demand (2) Price Regulation. Price Supports Twelve Color and Subsidies. The Concept of Videotapes Consumer and Producer Surplus, and Its Application to the Evalu- Introduction to the Economic ation of Government Regulatory Problem Policies. Production and Exchange in a Small Commune Economy. Introduc- 40-min. Color Videotape tion to Production Functions, 20-0105 Purchase $330 Rental $33. Production-Possibility Frontiers, and Supply and Demand. Production, Cost, and Theory 55-min. Color Videotape of the Firm (1) 20-0101 Purchase $385 Rental $39. The Theory of the Firm. Internal and External Costs. Production and Cost Minimization. The Cal- Theory of Demand culation of Cost Functions. Introduction to Consumer Demand. The Notion of "Utility". Utility 46-min. Color Videotape Maximization Subject to a Budget 20-0106 Purchase $360 Rental $36. Constraint. Introduction to In- difference Curves, and the Demand Curve of the Individual Consumer. Production, Cost, and Theory of the Fimn-÷2) 49-min. Color Videotape Short Run and_Long Run Cost 20-0102 Purchase $370 Rental $37. Curves. Marginal and Average Costs. Marginal and Average Revenues. How the Firm Maximizes Consumer Theory and Demand Profits. Behavior of the Demand Curve of the Individual Consumer Under 46-min. Color Videotape 20-0107 Purchase $360 Rental $36. Changing Prices and Income. The Market Demand Curve. Elastici- ties. Introduction to Market Structure 42-min. Color Videotape Pure Competition 20-0103 Purchase $340 Rental $34. Behavior of Competitive Firms. The Demand Curve as Seen by an Individual Competitive Firm. The Market Supply and Demand (1) Supply Curve of a Single Competi- Introduction to Supply and Demand. tive Industry. Equilibrium of Use of Supply-Demand Analysis to the Purely Competitive Firm and Solve a Variety of Economic Prob- Industry. lems. Shifts in Demand. Analyz- 45-min. Color Videotape ing the Incidence of a Tax. 20-0108 Purchase $355 Rental $36. 46-min. Color Videotape 20-0104 Purchase $360 Rental $36.

42 43 Monopoly Macroeconomics B avior of Monopolies. Profit Maximization by a Monopoly. Ten Color Government Regulation of a Monop- videotapes oly. Taxing a Monopoly. Introduction - Gross National Product and Income 45-min. Color Videotape 20-0109 Purchase $355 Rental $36. Introduction to Macroeconomics. Gross National Product and National Income. National In- come Accounting in the United Topics in Microeconomics (1) States. The Structure of American Indus- try. Monopoly, Oligopoly, and 46-min. Color Videotape Imperfect Competition. Measuring 20-0201 Purchase $360 Rental $36. Monopoly Power. Monopsony and Oligopsony. Aggregate Demand (1) 44-min. Color Videotape The Behavior of Aggregate Con- 20-0110 Purchase $350 Rental $35. sumption. Aggregate Demand. Disposable Income, Consumption, Savings, and Government Spending. Topics in Microeconomics (2) Introduction to the Multiplier. Factor Demand and Factor Pricing. 46-min. Color Videotape Market Structure and American 20-0202 Purchase $360 Rental $36, Industry. The Performande of American Industry.

48-min. Color Videotape Aggregate Demand (2) 20-0111 Purchase $365 Rental $37. Taxes and the Balanced Budget Multiplier. Deficit Spending and Fiscal Policy. The Use Group Discussion on Micro- of Fiscal Policy to Control economics the Economy. kound-Table Questions and Discussion. 51-min. Color Videotape 20-0203 Purchase $375 Rental $38. 33-min. Color Videotape 20-0112 Purchase $290 Rental $29.

MICROECONOMICS - Complete Set

Color Videotapes Study Guide Complete set of twelve Summaries, reproductions of Color Videotapes. overhead transparencies, 20-1100 Purchase $3670 (SAVE $550) problems, problem solutions, 60 Day Rental $382 (SAVE $42) final exam, and exam solutions. 268 pp. (One per student Suggested Text recommended.) No textbook is required for 20-2100 Purchase $11.50 each this subject, but Economics by (10% Discount on five or more.) Paul A. Samuelson, (McGraw- Hill) is recommended for students A Complete Self -Study Subject. who want an alternative treatment The set of videotapes described of the subject matter. 917 pp. above can be used as a complete self- study subject when accompanied by 20-3100 Purchase $12.95 each. the Study Guide.

43 44 MACROECONOMICS - Continued

Interest Rates and Investment Integration of Monetary and Investment Behavior in the Fiscal Policy United States. Interest Rates The Integration of Monetary ana and Investment Demand. The Fiscal Policy. Introduction to Notion of Present Discounted and Use of the IS-LM Apparatus. Value, and its Application to Monetary and Fiscal Multipliers. Bond Pricing. The Use of Monetary and Fiscal 54-min. Color Videotape Policy for Economic Stabilization. 20-0204 Purchase $385 Rental $39. 52-min. Color Videotape 20-0208 Purchase $380 Rental $38. Money and Commercial Banking The Notion of "Money". Excess Demand and Inflation The Operation of Commercial Excess Demand and Inflation. Banks. Commercial Banking and Unemployment. The Inflation- Money Creation. Unemployment Trade Off. Issues 42-min Color Videotape in Macroeconomic Policy. 20-0205 Purchase $340 Rental $34. 57-min. Color Videotape 20 -0209 Purchase $390 Rental $39. Federal Reserve System The Structure and Operation of Group Discussion on Macroeconomics the Federal Reserve System. How the Federal Reserve System Round-Table Questions and Controls the Money Supply. Discussion. 44-min. Color Videotape 43-min. Color Videotape 20-0210 Purchase $350 Rental $35. 20-0206 Purchase $355 Rental $36.

Demand and Supply of Money The Demand for Money in The U.S. Economy. Equilibrium of Money Demand and Supply. 59-min. Color Videotape 20-0207 Purchase $395 Rental $40.

MACROECONOMICS - Complete Set

Color Videotapes Study Guide Complete set of of ten Summaries, reproductions of Color Videotapes overhead transparencies, 20-1200 Purchase $3245-(SAVE $445) problems, problem solutions, 50 Day Rental $338 (SAVE $33) final exam, and exam solutions. 152 pp. (One per student Suggested Text recommended.) No textbook is required for 20-2200 Purchase $6.50 each. this subject, but Economics by (10% Discount on five or more.) Paul ,A. Samuelson, (McGraw- Rill) is recommended for students A Complete Self-Study Subject. who want an alternative treatment The set of videotapes described of the subject matter. 917 pp. above can be used as a complete self- study subject when accompanied by 20-3100 Purchase $12.95 each. the Study Guide.

44 4 5 Engineering Economy Sanford B. Thayer

Engineering Economy in concerned economic attractivenesss of with the economic analysis of investment proposals. investment alternatives. Fre- quently, there are several Many of the topics covered will technically feasible alternatives already be familiar from everyday which will satisfy the functional contact and no mathematics requirements of the task. But beyond simple arithmetic is used. only one of these is the most economically attractive alterna- tive. Sanford B. Thayer is Associate ,Professor of Mechanical Engineering A study of Engineering Economy at Colorado State University. provides students with the con- These materials were prepared at zepts and methodology necessary CSU and are offered by MIT as to evaluate the impacts of part of a cooperative effort in interest rates, income taxes, and education. timing of cash flows on the

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4.7 45 46 Engineering Economy

Ten Color Present Worth Method Videotapes Introduces the evaluation method which converts all cash flows to Introduction to Engineering Economy an equivalent amount today. The Provides an overview of the course example problem is present value and introduces the concept of of a U.S. Treasury Bond. "Time Value of Money." 27-min. Color Videotape 28-min. Color Videotape 23-0104 Purchase $250 Rental $25. 23-0101 Purchase $260 Rental $26.

Rate of Return Method Uniform Annual Cash Flow Method Introduces the evaluation method Introduces the evaluation method which solves for the prospective which converts all cash flows to rate of return on invested a time adjusted equivalent annual capital. The example problem amount. The example problem is utilizes a share of American the economic evaluation of solar Telephone and Telegraph Compar- energy for residential heating. common stock as the basis of 23-min. Color Videotape analysis. 23-0102 Purchase $220 Rental $22. 26-min. Color Videotape 23-0106 Purchase $245 Rental $25. Breakeven Analysis Introduces the concept of break- Benefit/Cost Method even to find the point where Introduces the engineering investments are equally attractive. economy method used by Federal, The example problem is the break- State, and local governments. even point of natural gas to make The example problem is the solar energy economically attrac- Benefit/Cost analysis of the tive for Solar House I at route for Interstate Highway 70, Colorado State University. near Vail, Colorado. 24-min. Color Videotape 25-min. Color Videotape 23-0103 Purchase $230 Rental $23. 23-0106 Purchase $240 Rental $24.

ENGINEERING ECONOMY - Complete Set

Color Videotapes Study Guide Complete set of ten Comments, reproductions of all Color Videotapes. graphics, reading assignments, problems, and problem solutions. 23-1100 Purchase $2100 (SAVE $235) 250 pp. (One per student 50 Day Rental $219 (SAVE $16) recommended.) Suggested Text 23-2100 Purchase $11.00 each. (104 Discount on five or more.) "Principles of Engineering Economy," by E.Grant and A Complete Self-Study Subject. W.Iresonv Ronald Press, 1970, The set of videotapes described 640 pp. above can be used as a coorpiete seif- 23-3100 Purchase $13.95 each. study subject when accaspanied by the Study Guide and Suggested Text. 46 47 Cost-Effectiveness Method 'Replacement Studies" Introduces a method of analysis Introduces the illtilodology neces- which allows alternatives to be sary to calculate the economc compared on the basis of costs timc to replace an asset that and criteria that cannot neces- still has a remaining physical sarily be expressed in monetary, life. The example problem uti- terms. The example problem lizes the replacement of an utilizes an economic evaluation automobile. of solar energy to produce 21-min. Color Videotape electrical energy. 23-0109 Purchase $205 Rental $21. 25-min. Color Videotape 23-0107 Purchase $240 Rental $24. Sources of Funds The lesson describes the common Effects of Income Taxes sources of funds to finance in- Introduces the effects of income vestment projects. The example taxes on engineering economy problem examines the financial decisions. The example problem statements of a corporation. utilizes an evaluation of the 20-min. Color Videotape economic attractiveness of de- 23-0110 Purchase $200 Rental $20. veloping a minimg site compared to selling a lease. 26-min. Color Videotape 23-0108 Purchase $245 Rental $25.

47 48 Friction, Wear and Lubrication Ernest Rabinowicz

Friction, Wear and Lubrication friction and its laws, the role is a coherent, up-to-date survey of lubricants, and such diverse of modern knowledge in this related topics as hardness, important area. Industry suffers surface energy, polishing, and tremendous losses each year because troubleshooting. of inefficient practices and ignorance in overcoming friction The only background required for and wear problems. And it is full appreciation of these the aim of this series to provide lectures and demonstrations is a quantitative information that first-year course in materials will be directly applicable to and in mathematics. solving these problems.

The major topics covered include Ernest Rabinowicz is Professor the various forms of wear, their of Mechanical Engineering at MIT. characteristics and, magnitudes,

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48 49 Friction, Wear and Lubrication

Twelve CoZor . Abrasive Wear Videotapes Derivation of the equation for abrasive wear, and of com- Tribology plications which modify it. The various topics that con- Evaluation of abrasive grain stitute the field of tribology and of abrasion-resistant sur- and their interrelation. The Remedies for avoiding technical literature. The con- faces. cept of material hardness and or minimizing abrasive wear. its influence on the area of 41-min. Color Videotape contact of surfaces. 18-0105 Purchase $335 Rental $34. 30-min. Color Videotape 18-0101 Purchase $275 Rental $28. Corrosive Wear Corrosive wear and its Wear characteristics. Possible Wear, its definition, its place benefits if corrosion product is both as a cause of loss of use- a lubricant. The causes of fulness and a process with many fretting and the quantitative uses. History of wear and des- laws governing material loss cription of the various types during fretting. The mechanism of wear. Discussion of the of polishing and of burnishing. surface energy of solids and the energy of adhesion of contacting 38-min. Color Videotape 18-0106 Purchase $320 Rental $32. surfaces.

32-min. Color Videotape Surface Fatigue Wear 18-0102 Purchase $285 Rental $29. The mechanism of surface fatigue wear and the laws governing it. Adhesive Wear Discussion of the Weibull dis- Presentation of the Archard tribution, its characteristics Erosive wear and its formulation of the law of and uses. adhesive wear, and discussion laws. The phenomena of fretting fatigue and its effect in re- of earlier work. Extensions and alternative formulations of ducing strength of structural Archard's equation. Evaluation members. of steps to be taken to reduce 37-min. Color Videotape adhesive wear. 18-0107 Purchase $315 Rental $32. 43-min. Color Videotape 18-0103 Purchase $345 Rental $35. Friction The history of friction, with Adhesive Particle Size emphasis on the roughness vs. Derivation of the equations for adhesion controversy. The laws the size of particles generated of friction and the extent to in adhesive wear. Experimental which they are obeyed. Friction confirmation. Influence of coefficient values and how they particle sizes with respect are measured. The magnitude of to surface roughness of sliding friction-induced temperature in- surfaces, and importance in creases. determining minimum clearance 38-min. Color Videotape of bearings. 18-0108 Purchase $320 Rental $32. 36-min. Color Videotape 18-0104 Purchase $310 Rental $31.

50 49 FRICTION, WEAR, and LUBRICATION - Continued

Stick-Slip Troubleshooting The relaxation and harmonic forms Systematic procedure for of frictional oscillations and troubleshooting, including how they arise. Conditions for determining the characteristics stick-slip and their relation to and function of the failed material properties. Methods of part; examination bf its preventing frictional oscil- sliding surface; and com- lations. Uses of stick-slip. putation of wear coefficient, temperature rise, and wear 43-min. Color Videotape particle size. Role of the 18-0109 Purchase $345 Rental $35. laboratory test in confirming a diagnosis. Some common tribological problems and Lubrication (1) methods of curing them. Fluid lubrication, boundary lubrication, and the types of 38-min. Color Videotape lubrication in between. 18-0112 Purchase $320 Rental $32. Lubricants which form coherent films, and those that reduce the surface energy. Characteristics of solid lubricant film. 43-min. Color Videotape 18-0110 Purchase $345 Rental $35.

Lubrication (2) Effect of reduction of surface energy on wear, and types of lubricants which are effective in this regard. Petroleum lubricants, synthetic lubricants, E. P. agents and their pro- perties. Automotive lubricants and additives. 45-min. Color Videotape 18-0111 Purchase $355 Rental $36.

FRICTION, WEAR AND LUBRICATION- Complete Set

Color Videotapes Study Guide Complete set of twelve Photographs, comments, reading Color Videotapes assignments, problems, problem 18-1100 Purchase $3405 (SAVE $465) solutions, and final exam. 60 Day Rental $356 (SAVE $35) 244 pp. (One per student recommended) Suggested Text 18-2100 Purchase $10.50 each. Friction and Wear of Materials (10% Discount on five or more) by Ernest Rabinowicz, John Wiley and. Sons, 1965. 244 pp. A Complete Self-Study Subeat. The setofvideotapes described 18-3100 Purchase $15.95 each above can be used ae a catripiets self- study itubjectiohen acoanpaniord by the StudyGuide,and! Suggested Text.

50 51 Introduction to Experimentation Ernest Rabinowicz

An Introduction to Experimentation Experimentation has been taught is a very practical series of lec- for some years at MIT as a tures and demonstrations on the technical discipline in its own designing, carrying out, and re- right. porting of experiments. The topics covered include the The mathematical level of this characteristics of instruments, series is not very high; some errors of measurement, statistical use is made of calculus in analysis of data, plotting deriving equations, but these can functional relationships, cor- be safely ignored by anyone more relation, and technical reporting. interested in application than theory. This systematic approach to mena- ingful experimentation can be applied with great benefit to a Ernest Rabinowicz is Professor wide variety of problems in of Mechanical Engineering at MIT. research and engineering.

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51 . 52 Introduction to Experimentation

Fourteen B&W 16w The Normal Distribution Films or Videotapes Deviation of the error compo- Experimentation nents for an external error esti- The various steps in an experi- mate. Error combinations pro- mental investigation. ducing distributions of measure- The his- ments about the mean. tory of experimentation. The The nor- human senses, their uses, and mal distribution and conditions how they are augmented by under which it arises. Uses of the normal distribution to esti- measuring instruments. Proper- ties of instruments. mate extreme values, and to eliminate data. 27-min. B&W Film or Videotape 15-0101 Purchase $180 Rental $20. 34-min. B&W Film or Videotape 15-0105 Purchase $225 Rental $23. Resolution of Instruments Discussion of sensitivity, Internal Error Estimate accuracy and resolution. Appli- Implications of a non-normal cation to the problem of meas- distribution and ways of adjust- suring foil thickness. Reso- ing it to normalcy. The error lution of the microscope. in the of the mean of a normal distri- focal plane and in depth. bution (standard error) and its Sensitivity and resolution of magnitude. Formula for internal the chemical balance. error. 32-min. B&W Film or Videotape 33-min. B&W Film or Videotape 15-0102 Purchase $215 Rental $22. 15-0106 Purchase $220 Rental $22.

Errors of Measurement Errors of the caliper micro- Computing the Standard Deviation meter and how they can be mini- Comparison of internal and ex- mized. Errors of the moving ternal error, and the optimum coil galvanometer and their way of combining them. Systema- individual characteristics. tic errors in measuring the Differences between random and velocity of light. Definitions systematic errors, unit and of precision and of accuracy. proportional errors. Reduction Method of computing the standard of errors of measurement by deviation a outlined, both when balancing or by partial balanc- number of data points is small ing. and when it is large.

37-min. B&W Film or Videotape 34-min. B&W Film or Videotape 15-0103 Purchase $240 Rental $24. 15-0107 Purchase $225 Rental $23.

Combination of Errors The y2 (Chi-Squared) Test Derivation of formula for ex- The x2 parameter defined, and ternal error propagation where adjustment for expended degrees quantities are multiplied to- of freedom explained. Use of gether. Analogy with aiming X2 in analysing coin tossing at a target. Corresponding experiments, a normal distribu- formula where quantities are tion, and the classic experi- ridded or subtracted. Formulae ments of Mendel. applied to a caliper micrometer and a speedometer. 30-min. B&W Film or Videotape 15-0108 Purchase $205 Rental $21. 30-min. B&W Film or Videotape 15-0104 Purchase $205 Rental $21.

52 53 The Poisson Distribution Correlation Application of the x2 tests to Procedures for detecting non- show personal error in esti- linearity. Plotting a non- mating final digits. Derivation linear function. Correlation, of the Poisson distribution and rank correion, and their use. explanation of its properties. Erroneous rdWults arising from Application of the Poisson dis- classification,procedures. tribution to the utilization of maternity hospitals. 31-min. B&W Film or Videotape 15-0112 Purchase $210 Rental $21. 31-min. B&W Film or Videotape 15-0109 Purchase $210 Rental $21. The Technical Report (1) Principle laid down that techni- The Best Straight Line cal report is main method of Methods of deriving the best conveying experimental results, straight line through a set of and that title and abstract are points. Discussion of the least sorting devices. Description of square method, with special the various sections of the re- reference to problems arising port, and comments on do's and when the x measurements have don'ts in connection with them. substantial error. 33-min. B&W Film or Videotape 29-min. B&W Film or Videotape 15-0113 Purchase $220 Rental $22. 15-0110 Purchase $195 Rental $20. The Technical Report (2) Plotting Other Functions Discussion of satisfactory Resolving choices when a number graphing methods. Peculiar of plotted functions will give a conventions surrounding techni- linear plot. Problem illustrated cal reports - data and pictures by plot of track records. Dis- are the best, narration has been cussion of methods of plotting tidied up.. Unacceptabld dis- the exponential function. tortions of the technical report - bad data edited out, unconven- 32-min. B&W Film or Videotape tional ideas suppressed, deli- 15-0111 Purchase $215 Rental $22. berate falsification. 33-min. B&W Film or Videotape 15-0114 Purchase $220 Rental $22.

INTRODUCTION TO EXPERIMENTATION -Complete Set

Pilms/Videotapes Study Guide Complete set of fourteen B&W Photographs, comments, reading 16 mm films or videotapes. assignments, problems, problem solutions, and final exam. 15-1100 Purchase $2685 (SAVE $300) 238 pp. (One per student 70 Day Rental $276 (SAVE $27) recommended.) Suggested Text 15-2100 Purchase $10.50 each. (10% Discount on five or more) An Introduction to Experimentation by E. Rabinowicz, Addison-Wesley, A Complete Self-Study Abject. 1970, 124 pp.411 The set eines/Videotapes described 15-3100 Purche $4.95 each. above can be used as a complete self - study subject when accompanied the Study Guide and'AggestedTexbyt.

53 Mechanics of Polymer Processing J. R. A. Pearson

Mechanics of Polymer Processing The introductory lectures and analyzes the mechanical behavior demonstrations in this series of polymer melts. Processing describe the structure and techniques for these melts have properties of polymers and emerged largely on an empirical illustrate some of the important basis, because their behavior has processing techniques. Later not been easy to describe. The lectures concentrate on the chemistry and physics of these fundamental mechanics of visco- plastics and elastomers has become elastic materials in terms of increasingly well understood. mathematical models and the But their most unusual properties application of these ideas to are mechanical , and these vary polymer processes. 'neatly -- with material, with temperature, and with type of deformation. J. R. A. Pearson is Professor of Chemical Engineering at Imperial College, University of London.

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55 Mechanics of Polymer Processing

Screw Extrusion of Pipe; In- Introduction jection Molding The screw extruder. Continuous Eight Color operation. Internal mechanism Videotapes for melting, mixing, pumping. Materials; Basic Processes Pipe extrusion through die. A Common commercial polymers by screw pre-plasticizedinjection chemical struture; hard or soft, molding machine. Cyclic cross-linked or thermoplastic. operation. Flow and cooling in Geometric variations in mold. products. Thermoplastic pro- cessing. Levels of knowledge; 38-min. Color Videotape molecular, microscopic, con- 21-0103 Purchase $320 Rental $32. tinuum. 43-min. Color Videotape Film Blowing; Blow Molding; 21-0101 Purchase $345 Rental $35. Thermoforming; Two-Roll Milling Biaxial extension of sheet in film blowing. Transient Physical Properties of Polymers fluctuation in continuous pro- Molecular concepts: long chains, cess. Extrusion for blow straight or'branched; side molding. Cyclic operation of groups; copolymers. blow mold. Thermal cycle in Statistical descriptions. thermoforming; plunger, vacuum Crystalline state. Glassy state. or pressure assisted. Mixing Rubbery state. Liquid state. and blending in 2-roll mill. Transitions. Supermolecular The rolling bank. effects. 41-min. Color Videotape 41-min. Color Videotape 21-0104 Purchase $335 Rental $34. 21-0102 Purchase $335 Rental $34.

INTRODUCTION - Complete Set

Color Videotapes Study Guide Complete set of eight Comments, photographs, repro- Color Videotapes ductions of overhead trans- parencies, reading assignments, 21-1100 Purchase $2460 (SAVE $275) problems, and solutions., 62 pp. 40 Day Rental $257 (SAVE $19) (One per student recommended.) Suggested Text 21-2100 Purchase $4.00 each (10% Discount on five or more,) Mechanical Principles of Polymer Melt Processing by A Complete Self -Study Subject. J.R.A. Pearson, MIT,1975, 148 pp. The set of videotapes dmgcribed 21-3000 Purchase $5.95 each. above can be amiss a complete self- study subject when accompanied by the Study Guide and Suggested Text.

55 5 6 INTRODUCTION Continued

Kinematics of Flow Processes Steady and unsteady flows. Con- Fundamentals of fined and free flows. Simple shear flow. Lubrication Polymer Melt Mechanics approximation. Extensional Twelve Color flows, uniaxial and biaxial. Videotapes 46-min. Color Videotape General Rheological Properties 21-0105 Purchase $360 Rental $36. Description of solid, fluid, viscoelastic solid, elastico- viscous liquid; types of Mathematical Models for Flow uniform deformation; simple Processes one-dimensional models. Fundamental laws. Field 49-min. Color Videotape variables. Approximations. 21-0201 Purchase $370 Rental,$37. Rheological equations of state. Uniaxial extensional flow Continuum Approach. dynamics. Steady simple shear Stress & dynamics. Deformation Orthogonal coordinate systems; 40-min. Color Videotape the nature of stress - a tensor; 21-0106 Purchase $330 Rental $33. displacement and deformation the strain, rate-of-strain and vorticity tensors. Stability of Flow Processes 49-min. Color Videotape Non-uniform and unstable flow. 21-0202 Purchase $370 Rental $37. Time and space fluctuations. Tube and channel flow Conservation Laws & Constitutive instabilities; entry, exit and Relations parallel flow effects. Sheet Conservation of mass, momentum drawing instability. and energy; rheological equations of state: elastic, 43-min. Color Videotape viscous, viscoelastic. 21-0107 Purchase $345 Rental $35. 47-min. Color Videotape 21-0203 Purchase $360 Rental $36. Control and Design of Flow Experimental Investigations Processes Density; specific heat; Control of existing processes. thermal conductivity. Shape and property fluctuations. Extrusion and shear rheology. Experimental Control variables. Film results for typical polymers. blowing as example. Surging in . extruders. Die design. Need 47-min. Color Videotape for fundamental information. 21-0204 Purchase $360 Rental $36. Quality control. The design process. Cost criterion. Viscometric Flow Simple shear flow; the cone- 48-min. Color Videotape and-plate viscometer; other 21-0108 Purchase $365 Rental $37. methods. Viscosity and normal stress differences. 46-min. Color Videotape 21-0205 Purchase $360 Rental $36.

Irrotational Flows Uniaxial extensional flow; pure shear flow; biaxial extensional flow; extensional viscosity and other rheological functions. 42-min. Color Videotape 21-0206 Purchase $340 Rental $34.

56 Dynamic Viscosity The Lubrication Approximation Complex modulus; values for General theory; simple example simple models; time-temperature of wedge flow; applications. superposition. Linear and non- 40-min. Color Videotape linear viscoelastic models. 21-0211 Purchase $330 Rental $33. 46-min. Color Videotape 21-0207 Purchase $360 Rental $36. Thin Sheet Approximations General Theory; continuity and stress equilibrium equations; Unsteady Flows flat sheet flow; simple plane Die swell; elastic recovery; flow example; applications. melt fracture and flow instability. 44-min. Color Videotape 21-0212 Purchase $350 Rental $35. 56-min. Color Videotape 21-0208 Purchase $390 Rental $39. Application to Basic Solution: Confined Polymer Processing Flow (1) Pressure flow in uniform Twelve Color channel; flow calculations for Videotapes known fluid; channel flow as Introduction rheological measurement. Objectives of polymer processing geometrical, physical and chemi- 41-miriColor Videotape cal; control of process; impor- 21-0209 Purchase $335 Rental $34. tance of thermal history; types of process confined and free flows. Basic Solution: Confined Flow (2) 49-min. Color Videotape General uniform channel flow 21-0301 Purchase $370 Rental $37. between parallel flat moving plates. Temperature Effects in Confined 43-min. Color Videotape Flows 21-0210 Purchase $345 Rental $35. The lubrication approximation; simple example of plane flow; dimensionless groups; scale temperatures and process variables.

f 47-min. Color Videotape 21-0302 Purchase $360 Rental $36.

FUNDAMENTALS - Complete Set

Color Videotapes Study Guide Complete set of twelve Comment4, PhotographOi 'repro- Color Videotapes. duCtione of overhead:trans parencies, reading assignments, 21-1200 Purchase $3845 (SAVE $575) Problems, and OolutiOns0 112 PP. 60 Day Rental $400 (SAVE $44) (00e per student reCommended.) Suggested Text 21 -2100 Purdhaie $5.00 eaCh.- (10% Discount on five or Mechanical Principles of Polymer Melt Processing by AComplateSelf-Study .5144,Wt. J.R.A, Pearson, MIT,1975. 148 pp. Theset ofvideotapiae:dstiori.bed 21-3000 Purchase $5.95 each. above can be used as a comploted self- study subject whe$ accompanied by the Study Guide and. Suggested TOrt.

57 58 APPLICATIONS - Continued

Flow in Dies Fiber Spinning: General Forms of extrudate; .symmetrical One dimensional model; conserva- extrudates; quantitative analysis; tion equations; dimensionless use of dimensionless variables; representation and groups; simple example; instability in steady-state equations; boundary die flow. conditions. 47-min. Color Videotape 47-min. Color Videotape 21-0303 Purchase $360 Rental $36. 21-0307 Purchase $360 Rental $36.

Single Screw Extruder: Metering Fiber Spinning: Stability Zone Linearized perturbation analysis; The extruder overall; geometrical Fourier decomposition; sensitivity simplifications; velocity profiles; analysis for various imposed dimensionless groups; approximate disturbances; stability analysis theories; numerical solutions and and draw resonance. computer programs. 52-min. Color Videotape 47-min. Color Videotape 21-0308 Purchase $380 Rental $38. 21-0304 Purchase $360 Rental $36.

Film Blowing: Steady-State Single Screw Extruder: Melting Symmetric Zone Steady axisymmetric flow; Basic models; the plug-pool model geometrical approximations; with its five zones solid bed, balance equations for mass, force melt pool, swept melting layer and energy; rheological relations; and growing lubricating layers; purely viscous model; extensions. mass and stress balances; surging. 48-min. Color Videotape 57-min. Color Videotape 21-0309 Purchase $365 Rental $37. 21-0305 Purchase $390 Rental $39.

Single Screw Extruder: Feed Zone; Scale-up Solid plug models; complete model for plasticating extruders; scaling-up extruders. 57-min. Color Videotape 21-0306 Purchase $390 Rental $39.

APPLICATIONS - Complete Set

Color Videotapes Study Guide Complete set of twelve Step-by-step path through the Color Videotapes. material with summaries of the 21-1300 Purchase $3840 (SAVE $575) lectures, photographs, problems sh 60 Day Rental $400 (SAVE $44) and problem solutions. 108 pp. (One per student recommended.) Suggested Text 21-2300 Purchase $4.50 each. Mechanical principles of Polymer (10% Discount on five or more.) Melt Processing by J.R.A. Pearson, MIT.1975, 148 pp. A Complete Self-Study Subject. The set of videotapes described 21 -3000 Purchase $5.95 each. above can be used as a complete self- study subject when accompanied by the Study Guide and Suggested Text.

58 59 Film Blowing: Stability. Film Injection Molding Casting General remarks on process; flow Linearized analysis for sensiti- in molds - unsteady and high vity and stability of viscous pressure drop; simple example film-blowing model; unsteady of disc mold; flow equations; axisymmetric and steady non- freezing; complexity of axisymmetric disturbances. rheological forces involving Kinematic model for film casting; simple shear and irrotational growth of edge bead; linearized distortion; instability of flow. sensitivity and stability analysis. 51-min. Color Videotape '48-min. Color Videotape 21-0312 Purchase $375 Rental $38. 21-0310 Purchase $365 Rental $36.

Calendering Narrow channel approximation; simple plane flow equations; difficulty in specifying inlet and exit boundary conditions; mixing; load on rolls; instability. 43-min. Color Videotape 21-0311 Purchase $345 Rental $35.

59 GO Modern Control Theory Michael Athans

Modern Control Theory is an developed to analyze an important engineering discipline which deals class of practical problems and to with specific analytical and design' suitable control systems. algorithmic methods which can be The basic pre-requisite for these used to control complex stochastic lectures and demonstrations is a dynamic systems so as to optimize working knowledge of vectors and their performance. These tools matrices and their operations as have found wide applicability in well as an exposure to the notion aerospace and defense systems, of eigenvalues and eigenvectors. industrial control systems, transportation systems, biological systems, power systems, and socio- Michael Athans is Professor of economic systems. Electrical Engineering and Computer Science at MIT and In addition to the theory, a set Director of the Electronic of computer subroutines has been Systems Laboratory.

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6o*04110' 61 Modern Control Theory

The General Notion of the State System Analysis of a Dynamical System Introduction of state variables in Eleven Color an input-output representation. Videotapes Input-state-output description of Introduction to Optimal Control lumped systems using vector and Estimation Methods (1) differential or difference Overview of philosophy of modern equations. control. Definition of deter- ministic optimal control, 45-min. Color Videotape stochastic estimation, and 19-0101 Purchase $355 Rental $36. stochastic control. 49-min. Color Videotape Linear Continuous Time Dynamical 19-0001 Purchase $370 Rental $37. Systems Systems described by linear, constant or time-varying, vector Introduction to Optimal Control differential equations. Solution and Estimation Methods (2) methods; the state transition Block diagram description of final matrix and the matrix exponential. engineering design using the Forced and unforced solutions. methods of modei-n control theory. 42-min. Color Videotape 36-min. Color Videotape 19-0102 Purchase $340 Rental $34. 19-0002 Purchase $310 Rental $31.

SYSTEM ANALYSIS - Complete Set

Color Videotapes Computer Card Deck Complete set of eleven Set of punched cards in Fortran Color Videotapes. for implementing programs described in Computer Manual. 19-1100 Purchase $3295 (SAVE $450) 55 Day Rental.$342 (SAVE $34) 19-5000 Purchase $40.00 each.

Suggested Text Study Guide Optimal Control, by M. Athans Reproductions of overhead trans- and P.L. Falb, McGraw-Hill, parencies, comments, readings, 1966, 879 ,PP. problems and problem solutions. 19-3100 Purchase $21.00 each. 192 pp. (One per student recommended.) CoolerManual 19-2100 Purchase $8.50 each. An especially written manual of (10% Discount on five or more.) computer subroutines. 208 pp. A Complete Self-Study Subject. 19-4000 Purchase $9.00 each. The set of videotapes described (10% Discount on five or more.) above can be used as a complete self- study subject when accompanied by the Study Guide, Computer Manual, and Suggested Text.

61 62 SYSTEM ANALYSIS - Continued

Dynamic Linearization for Controllability and Observability Continuous Time Systems Definitions and tests for control- The notion of a nominal trajectory lability and observability. for nonlinear systems. Pertur- Physical interpretation of these bation methods and Taylor series fundamental concepts. expansions for vector-valued nonlinearities. The linear 50-min. Color Videotape dynamic perturbation model. 19-0108 Purchase $375 Rental $38. 27-min. Color Videotape 19-0103 Purchase $250 Rental $25. Computer Routines for Linear System Analysis Use of computer subroutines for Discrete-Time Dynamical Systems calculating solutions of linear Perturbation and dynamic linear- dynamic systems. A helicopter ization methods for systems des- example. cribed by nonlinear vector dif- ference equations. 38-min. Color Videotape 19-0109 Purchase $320 Rental $32. 40-min. Color Videotape 19-0104 Purchase $330 Rental $33. Deterministic Optimal Control Linear Time Invariant Dynamical Ten Color Systems Videotapes Review of eigenvalues and eigenvectors; their role in the General Discussion expression of solutions of linear Motivation for optimal control differential and difference problems. Counterintuitive equations. Definition of, and examples. Relevance of scalar tests for, stability. valued criteria for performance. 52-min. Color Videotape 49-min. Color Videotape 19-0105 Purchase $380 Rental $38. 19-0201 Purchase $370 Rental $37.

The Minimum Principle of The Relation of Transfer Functions Pontryagin: Continuous Time and State Variable Representations Case Review of Laplace transforms for Statement of the Pontryagin scalars, vectors, and matrices. minimum principle for different Techniques for obtaining the formulations of optimal control transfer matrix and transfer problems. function from state space re-' presentations. Relationships of 49-min. Color Videotape poles, zeros, and matrix eigenvalues. 19-0202 Purchase $370 Rental 7,37. 53-min. Color Videotape The Dynamic Programming Algorithm 19-0106 Purchase $380 Rental $38. Discrete-time optimal control problems. The principle of optimality. Bellman's dynamic From Transfer Functions to State programming algorithm and Variable Representations its implementation. Systematic techniques for trans- 60-min. Color Videotape forming a transfer function to 19-0203 Purchase $395 Rental $40. different state variable realiza- tions. Illustrations using analog computer diagrams. The Minimum Principle: Discrete Time Case 41-min. Color Videotape Discrete optimal control 19-0107 Purchase $335 Rental $34. problems and the associated minimum principles for their solutions. 43-Min. Color Videotape 19-0204 Purchase $345 Rental $35.

62 6.3 The Steepest Descent Method Description of a "simple" Deterministic Optimal digital computer algorithm Linear Feedback to solve deterministic optimal control problems. Twenty-one CoZor Videotapes 84-min. Two Color Videotapes Motivation for the Linear-Quad- 19-0205 Purchase $555 Rental $60. ratic Problem Detailed motivation for using quadratic performance criteria Numerical Example: Solution for the optimal control of the of a Minimum Fuel Problem linearized perturbational dynam- in the Apollo Project ics about a nominal trajectory Illustration of the steepest associated with a nonlinear descent method to solve an system. The nature of the opti- orbit transfer problem involving mal linear-quadratic solution; the Apollo SSV orbiter stage. state perturbation linear feed- 21-min. Color Videotape back. 19-0206 Purchase $210 Rental $21.. 73-min. Two Color Videotapes 19-0301 Purchase $480 Rental $48. Newton's Method General philosophy of the Newton The Solution of the Linear-Quad- or quasilinearization method. ratic Problem Reduction of minimum principle Statement of the Linear-Quadratic equations to the two-point- problem for both continuous and boundary value problem, and discrete time systems. Solution their iterative solution using methods via Riccati equations. Newton's method. Summary of off-line and on-line 83-min. Two Color Videotapes computations. 19-0207 Purchase $500 Rental $50. 47-min. Color Videotape Minimum Principle vs Dynamic 19-0302 Purchase $360 Rental $36. Programming Contrast from a technical and algorithmic viewpoint of the two methods for solving optimal control problems. Open-loop vs closed-loop optimal controls. 50-min. Color Videotape 19-0208 Purchase $375 Rental $38.

DETERMINISTIC OPTIMAL CONTROL - Complete Set

Videotapes Study Guide Complete set of ten Reproductions of overhead trans- Color Videotapes. parencies, comments, readings, 19-1200 Purchase $2745 (SAVE $375) problems and problem solutions. 50 Day Rental $289 (SAVE $29) 306 pp. (One per student recommended.) Suggested Text 19-.2200 Purchase $13.00 each. (10% Discount on five or more.) Optimal Control,by M. Athans and P.L. Falb, McGraw-Hill, 1966, 879 pp. A Complete SelP;Study Subject. The set of videotapes described 19-3200 Purchase $21.00 each. above can be used as a complete self- study subject when accompanied by the Study Guide, and Suggested Text.

63 6 DETERMINISTIC OPTIMAL LINEAR FEEDBACK - Continued

Motivation for the Steady-State The Steady-State Linear-Quadratic Linear-Quadratic Problem Problem with Deterministic Static linearization; state-input Disturbances equilibria and their optimal Modelingof exogeneous distur- calculation. Formulation of the bances using uncontrollable optimal dynamic control problem state variable motels. Solution using linearized perturbation of the regulation problem. dynamics. Influence of the disturbances in the overall control structure 104-min. Three Color Videotapes and their decoupling in the 19-0303 Purchase $885 Rental $89. control system design. 41-min. Color Videotape The Steady-State Linear-Quadratic 19-0306 Purchase $335 Rental $34. Problem: Continuous-Time Case Problem definition and the nature of the optimal solution via the Control of Helicopter at Hover algebraic Riccati equation. Problem formulation and solution Constant gain state variable for the design of an autopilot feedback designs and their guaran- to keep a helicopter at a desired teed stability. hovering condition. How to select the performance index for 51-min. Color Videotape physical problems. 19-0304 Purchase $375 Rental $38. 31.-min. Color Videotape 19-0307 Purchase $280 Rental $28. The Steady-State Linear-Quadratic Problem: Discrete Time Case The optimal control of linear Programs: Helicopter Example discrete-time systems with Use of the computer subroutines respect to quadratic performance to solve for the optimal feed- indices over an infinite time horizon. back gain for a helicopter The discrete algebraic hovering problem. Riccati equation. Stability of the closed loop designs. 40-min. Color Videotape 38-min. Color Videotape 19-0308 Purchase $330 Rental $33. 19-0305 Purchase $320 Rental $32.

DETERMINISTIC OPTIMAL LINEAR FEEDBACK - Complete Set Computer.Card Deck Color Videotapes Set of punched cards in Fortran Complete set of twenty-one for implementing programs Color Videotapes. described in Computer. Manual. 19-1300 Purchase $5505 (SAVE $890) 100 Day Rental $572 (SAVE $70) 19-5000 Purchase $40.00 each. Study Guide Suggested Text A step-by-step path through the _Optimal Control, by M. Athans material with viewgraph re-

and P. Falb, McGraw Hill, 1966, productions, comments, exercises, 878 pp. and solutions. 305 pp. (One 19-3100 Purchase $20.00 each. per student recommended.) 19-2300 Purchase $13.50 each. Computer Manual (10% Discount on five or more.) A Complete Self -Study &West. An especially written manual of The set of videotapes described cOmputer subroutines. 208. pp. above can be used as a mompaete self- 19-4000 Purchase $9.00 each. study subject when accompanied by (10% Discount on five or more.) the Study Guide, Computer Manual and Suggested Text.

64 65 The Steady-State Linear Regulator Air Traffic Control in the Near Problem for Constant Disturbances Terminal Area Proper formulation of the opti- A numerical example that illus- mization problem for the design trates how the solution of of linear quadratic regulators three distinct optimization in the presence of constant problems can be used to obtain disturbances. The need to incor- optimal path stretching and porate a penalty on the control . route control strategies to land rates in the cost functional. aircraft under both normal and The existence of integrators in emergency conditions. the optimal feedback design. 152-min. Three Color Videotapes 70-min. Two Color Videotapes 19-0313 Purchase $1000 Rental $100. 13 -0309 Purchase $465 Rental $47. Computer Routines for Determi- nistic Optimal Linear Feedback Design of Proportional-Deriva- Use of computer subroutines for tive-Integral Controllers for computing the solution to the Tracking Step Inputs steady-state linear-quadratic Appropriate formulation of problem. A helicopter example. optimal linear-quadratic designs 45-min. Color Videotape that can follow multivariable 19-0314 Purchase $355 Rental $36. step inputs with zero steady- state error. Realization using state integral feedback plus Stochastic Estimation proportional and integral chan- Twenty Color nels on the vector error signals. Videotapes 44-min. Color Videotape Introduction 19-0310 Purchase $350 Rental $35. Definition of the stochastic estimation problem. Physical problems. Mathematical models. Colored and white noise models. Asymptotic Behavior of Steady- State Linear-Quadratic Closed- 47-min. Color Videotape Loop Systems 19-0401 Purchase $360 Rental $36. General properties of optimal linear-quadratic designs on the weights in the cost functional Review of Probabilistic Concepts charge; motion of the optimal Random variables; expected values, closed loop poles in the s-plane. variances, covariances, and Effect of minimum and non- correlations. Joint and condi- minimum phase zeros. tional probabilities, conditional expectations and covariances. 77-min. Two Color Videotapes Extension of concepts to vector 19-0311 Purchase $510 Rental $51. and matrix valued random variables. Optimal Control of a Macro- 50-min. Color Videotape economic Model of the U.S. 19-0402 Purchase $375 Rental $38. Economy (1957-1962) An economic example ofusing optimal linear-quadratic optimal Response of Linear Systemsto feedback control strategies to White Noise Inputs: Discrete control, in different ways, a Time Case model of the U.S. economy Discrete white noise. Open loop developed by R.S. Pindyck. mean and covariancepropagation for systems described by vector 44-min. Color Videotape difference equations. Transient 19-0312 Purchase $350 Rental $35. and steady behavior. Prediction and forecasting. 46-min. Color Videotape 19-0403 Purchase $360 Rental $36. 6; 65 STOCHASTIC ESTIMATION - Continued

Response of Linear Systems to The Discrete-Time Kalman Filter White Noise Inputs: Continuous Formulation of the state esti- Time Case mation problem for linear dis- Open-loop prediction and fore- crete-time dynamic systems casting for systems described by described by stochastic vector linear vector differential difference equations, given equations. Dynamic evolution noisy measurements of linear of means'and covariance matrices. combinations of state variables. Steady state considerations. The discrete Kalman filter; predict and, update formulas for 52-min. Color Videotape the conditional mean of the 19-0404 Purchase $380 Rental $38. state and covariance matrices. 86-min. Two Color Videotapes The Bayesian Approach to 19-0406 Purchase $570 Rental $57. Parameter. Estimation Prior and posterior information. Mathematical modeling of multi- Effect of Changing Covariance variable static experiments. Matrix of Measurement upon a Bayes rule and the relation of Kalman Filter prior and posterior (conditional) A four dimensional numerical probability density functions. example that illustrates Linear-gaussian estimation dynamic evolution of error problems. Formulas that deter- covariances as a function of mine the updated means and number of measurements and of covariance matrices. the value of the measurement covariance matrix. 90-min. Two Color Videotapes 19-0405 Purchase $595 Rental $60. 36-min. Color Videotape 19-0407 Purchase $310 Rental $31.

STOCHASTIC ESTIMATION - Complete Set

Color Videotapes Computer Card Deck Complete set of twenty Set of punched cards in Fortran Color Videotapes. for implementing programs 19-1400 Purchase $5725 (SAVE $925) described in Computer Manual. 95 Day Rental $596 (SAVE $75) 19-5000 Purchase $40.00 each. Suggested Text Lecture Notes Applied Optimal Estimation by To be published. Write for A. Gelb, MIT Press, 1974, 374 pp. price and information. 19-3400 Purchase $7.95 each. ,A Complete Self-StudY, Subject. Computer Manual The set of videotapes described An especially written manual of above can be used as a complete self- computer subroutines. study subject when accompanied by 208 pp. the Lecture Notes, Computer Manual. 19-4000 Purchase $9.00 each. and Suggested Text. (101 Discount on five or more.)

66

6 7 The Steady-State Kalman Filter: The Continuous Time Kalman-Bucy Discrete Time Case Filter Asymptotic behavior of the Definition of the state discrete Kalman filter for time- estimation problem for stochastic invariant systems and stationary dynamic systems described by noise statistics. Constant gain linear time-varying vector Stability differential equations, given realizations. linear measurements of the properties. state variables in the presence 43-min. Color Videotape of additive measurement noise. 19-0412 Purchase $345 Rental $35. The Kalman-Bucy filter; the Riccati equation for dynamic propagation of the error Numerical Example: Estimation covariance matrix. of positions, velocities, and 48-min. Color Videotape accelerations 19-0408 Purchase $365 Rental $37. A numerical example using con- stant acceleration inertial dynamics to illustrate the The Steady-State Kalman-Bucy structure and accuracy of the Filter: Continuous Time Case Kalman-Bucy filter. Asymptotic behavior of the Kalman-Bucy filter under assump- 32-min. Color Videotape tions of time-invariant 19-0413 Purchase $285 Rental $29. dynamics and stationary noise statistics. Stability proper- Numerical Example: Sensor ties. The algebraic Riccati Tradeoffs equation. Illustration of using the Kalman filtering theory for deciding 446-min. Color Videotape 19-0409 Purchase $365 Rental $37. the best sensor to use for fixed dynamics.

Steady-State Programs: 47-min. Color Videotape Helicopter Example 19-0414 Purchase $360 Rental $36. Description of the digital com- puter subroutines for solution Suboptimal Nonlinear Filtering of steady-state Kalman-Bucy Algorithms: Discrete-Time filtering problems, and the Definition of nonlinear estima- stochastic simulation of the tion problem. Computational resulting system.An illustra- difficulties of optimal estima- tive example using helicopter tion algorithm. Suboptimal dynamics. algorithms: the extended Kalman 40-min. Color Videotape filter. Real time - 'computational 19-0410 Purchase $330 Rental $33. requirements. 87-min. Two Color Videotapes 19-0415 Purchase $575 Rental $58. A Visualization of Kalman Filtering An illustrative example using Numerical Example: Estimation computer generated graphics of of position, velocity, and the Kalman filter using a doubly ballistic parameter for a hinged pendulum. vertical re-entering body Numerical example illustrating 40-min. Color Videotape how bias estimation errors 19-0411 Purchase $330 Rental $33. associated with the use of an extended Kalman filter, can be removed through the use of a second order filter. 47-min. Color Videotape 19-0416 Purchase $360 Rental $36.

67 6 3 STOCHASTIC ESTIMATION- Continued

Computer Routines for Linear The Discrete-Time Linear- Stochastic Estimation Quadratic-Gaussian (LQG) Problem Use of computer routines to Optimal stochastic control for design and simulate the steady- linear time-varying stochastic state Kalman-Bucy filter. A systems described by vector helicopter example. difference equations and noisy 54-min. Color Videotape measurements. The Gaussian 19-0417 Purchase $385 Rental $39. assumption. Quadratic criteria. The separation theorem. The optimal linear feedback compen- Stochastic Control sator. Analysis of the optimal cost-to-go. Sixteen Color Videotapes 83-min. Two Color Videotapes Introduction 19-0503 Purchase $580 Rental $58. Overview of stochastic control problem. Typical application areas. General discussion of The :Continuous-Time Linear- stochastic optimal control Quadratic-Gaussian (LQ)'Problem problems and of their solution. Formulation and solution of the- optimal stochastic control 40-min. Color Videotape problem for linear time-varying 19-0501 Purchase $330 Rental $33. dynamic systems described by stochastic vector .differential equations. Quadratic perfor- mance criteria. The General Problem Gaussian ran- Precise formulation of optimal dom processes. The separation stochastic control problems for theorem. The structure of the optimal linear feedback dynamic nonlinear dynamical systems compensator. The control and describedby discrete-time stochastic vector difference filtering matrix Riccati equations. equations'. Stochastic dynamic programming. Conditional 87-min. Two Color Videotapes expectations and the classical 19-0504 Purchase $575 Rental $58. information pattern. Compu- tational difficulties. 89-min. Two Color Videotapes 19-0502 Purchase $59n Rental $59.

STOCHASTIC CONTROL - Complete Set

Color Videotapes Computer Card Deck Complete set-of sixteen Set of punched cards in Fortran Color Videotapes. for implementing programs 19-1500 Purchase $4270 (SAVE $640) described in Computer Manual. 75 Day Rental $442 (SAVE $49) 19-5000 Purchase $40.00 each.

Computer Manual Lecture Notes An especially written manual of To be published. Write for computer subroutines. 208 pp. price and information.

19-4000 Purchase $9.00 each. A Complete Self-Study Subject. (10% Discount on five or more.) The set of videotapes described above can be used as a complete self- study subject when accompanied by the Lecture Notes and Computer Manual.

68

69 Numerical Example of LQG Design Steady State Theory Computer for a Third Order Continuous Programs: Helicopter Example Time System Description of the computer The numerical characterization subroutines that solve and of the optimal LQG dynamic simulate steady state LQG designs. compensator for a specific Illustration using a helicopter numerical example. example. 27-min. Color Videotape 57-min. Color Videotape 19-0505 Purchase $250 Rental $25. 19-0509 Purchase $390 Rental $39.

Systematic Procedures and Control of a Nonlinear System Numerical Example about Desired Constant Equilib- Numerical solution of a fourth rium order continuous time LQG Step-by-step procedures for the example. Structure of resulting suboptimal design of a control optimal dynamic compensator. system for maintaining a time invariant nonlinear dynamic 38-min. Color Videotape system abolit a. desired constant 19-0506 'Purchase $320 Rental $32. input-state equilibrium.

39-min. Color Vid'eotape Control of a Nonlinear System 19-0510 Purchase $325 Rental $33.

About Desired Time Varying . Trajectory -,----- Step-by-ste0 procedures for the Optimal Control of the F-8 suboptimal st.ochastic.control Aircraft of nonlinear SyStems described Visualization of LQG based con- by stochastic vector differential trol of the longitudinal dynam- equations. The blending of ics of the F-8 aircraft, subject open-loop optimal controls and to wind gusts, using computer LQG designed feedback compensa- generated images. tors. 40-min. Color Videotape 52-min. Color Videotape 19-0511 Purchase $330 Rental $33. 19-0507 Purchase $380 Rental $38. Computer Routines for Linear The Steady State LQG Problem: Stochastic Control Continuous Time Case Use of computer routines to Formulation and solution of the design and simulate the steady- optimal stochastic control prob- state stochastic regulator lem for linear time-invariant using the LQG approach. 'dynamic systems with respect to 57-min. Color Videotape quadratic performance criteria 19-0512 Purchase $390 Rental $39. and with stationary Gaussian noises. The linear time-invar- iant LQG feedback compensator and the separation property of the closed loop poles. Rules of thumb for design. 68-min. Two Color Videotapes 19-0508 Purchase $450 Rental $45.

69 70 Network Analysis and Design Aram Budak

Network Analysis and Design in ,used to study the characteristics the Frequency Domain is intended of many practical circuits. for circuit designers who want to learn about modern operational This course assumes knowledge of amplifiers. The first set of Laplace transformation and funda- lectures and demonstrations mentals of circuit theory. develops a number of useful circuit analysis techniques and applies these to a large number of sample Aram Budak is Professor of Electrical problems. Engineering at Colorado State University. These materials were In the second set, RC-operational prepared at CSU and are offered amplifier circuits are discussed. by MIT as part of a cooperative Ideal and one-pole rolloff modeling effort in education.' of operational amplifiers are

70 71 Network Analysis and Design

Ladder Networks The Frequency Domain RC, RL, LC, and Parallel Ladder Structures. ,7-!ght Color Videotapes 49-min. Color Videotape 24-0105 Purchase $370 Rental $37. Useful Circuit Analysis Techniques (1) Discussion and application of Natural and Forced Response the principle of superposition. Decomposition of the response into its natural and forced 33-min. Color Videotape 24-0101 Purchase $290 Rental $29. components. Demonstration of the two components of the res- ponse. Useful Circuit Analysis 39-min. Color Videotape Techniques (2) 24-0106 Purchase $325 Rental $33. Determination of eqUivalent circuits. Step and Sinusoidal-Steady-State 32-min. Color Videotape $22. Response 24-0102 Purchase $215 Rental Calculation of step. and sinusoidal response of networks. Dependent Sources 36-min. Color Videotape Analysis techniques involving 24-0107 Purchase $310 Rental $31. dependent sources. 40-min. Color Videotape 24-0103 Purchase $330 Rental$33. Magnitude and Phase Determination and interpretation of magnitude and phase characteris- Demonstration of response The System Function' tics. Discussion of poles, zeros,and near complex poles and complex. system functions. zeros. PG 43-min. Color Videotape 46-min. Color Videotape 24-0104 Purchase $345 Rental$35. 24-0108 Purchase $360 Rental $36.

THE FREQUENCY DOMAIN - Complete Set

dolor Videotapes Study. Guide Comments, chalkboard photographs, . Complete set of eight Color Vi&otapes. reading assignments, problem solutions. 65 pp. (One per 24-1100 Purchase $2290 (SAVE $255) student recommended.) 40 Day Rental $238 (SAVE $18) 24-2100 Purchase $4.00 each. Suggested Text (10% Discount on five or more.) Passive and Active Net0Ork Analysis and Synthesis by A COMplete Self -Study Subject, A. Budak, Houghton Mifflin, The set orvideotapes described 1974, 733 pp. above can be used as a complete self-: study subject when accompanied by 24-3100 Purchase.$17..-95 each. the Study Guide and Suggested Text.

71 72 Frequency Response The Operational Amplifier Frequency response of inverting and noninverting amplifiers. Twelz,e Color Videotapes Demonstrations of the magnitude vs. frequency curves and the The Ideal Operational Amplifier measurement of the gain-bandwidth Modeling of the ideal operational product. amplifier. 35-min. Color Videotape 39-min. Color Videotape 24-0205 Purchase $305 Rental $31. 24-0201 Purchase $325 Rental $33. Bandwidth Linear Applications (1) Comparison of bandwidth for single Analysis of inverting, non- and multistage amplifier circuits. inverting, difference, and other Demonstration of extension of amplifier circuits. bandwidth with a capacitor. 41-min. Color Videotape 34-min; Color Videotape 24-0202 Purchase $335 Rental $34. 24-0206 Purchase $300 Rental $30.

Linear Applications (2) Step Response Operational amplifier circuits Relationship between pole position for producing variable impedance, and rise time. Demonstration of grounded current source, and ramp generator. bandpass filtering. 32-min. Color Videotape 49-min. Color Videotape 24-0207 Purchase $285 Rental $29. 24-0203 Purchase $370 Rental $37.

Output Impedance The One-Pole Rolloff Model Output equivalent circuit of Discussion of the one-pole rolloff amplifiers. Demonstration of the model- output impedance vs. frequency 39-min. Color Videotape characteristic. 24-0204 Purchase $325 Rental $33. 41-min. Color Videotape 24-0208 Purchase $335 Rental $34.'

THE OPERATIONAL AMPLIFIER - Complete Set

Color Videotapes Study Guide Complete set of twelve Comments, chalkboard photographs, Color Videotapes. reading assignments, problem solutions. 100 pp. (One per 24-1200 Purchase $3395 (SAVE $465) 60 Day Rental $356 (SAVE $35) student recommended.) Suggested Text 24-2200 Purchase $6.00 each (10% Discount on five or more.) Passive and Active Network Analysis and Synthesis by A Complete Self-Study Subject. A. Budak, Houghton Mifflin, The setofvideotapes described 1974, 733 pp. above can be used as a complete self- 24-3100 Purchase $17.95 each. study subject when accompanied by the Study Guide and Suggested Text.

72 Ideal and Actual Frequency Response Nonlinear Applications (1) Bandwidth and rise-time improvement Operational amplifier circuits with negative capacitance. using the nonlinear model of Demonstration of the effect of operation. Demonstration of the negative capacitance. response of the dead-zone amplifier. 35-min. Color Videotape 24-0209 Purchase $305 Rental $31. 41-min. Color Videotape 24-0211 Purchase $335 Rental $34. Offset, Slewing, and Dynamic Range Discussion of limitations of Nonlinear Applications (2) integrated-circuit operational Applications involving diodes and amplifiers. Demonstration of operational amplifier circuits. voltage-and current-limited Demonstration of the characteris- response. tics of a fullwave rectifier circuit. 41-min. Color Videotape 24-0210 Purchase $335 Rental $34. 35-min. Color Videotape 24-0212 Purchase $305 Rental $31.

73 Nonlinear Vibrations Jacob P. Den Hartog

Nonlinear Vibrations describes destruction. These and many various methods -- exact and other problems of great practical approximate, numerical and importance can only be understood graphical -- for dealing with in terms of nonlinear vibration vibrations in systems described theory. by nonlinear differential equations. Although 95 per cent It is the purpose of this series of vibrational problems can be to use the simplest possible analyzed with the aid of linear mathematics while keeping the

vibration theory, there is a . physical interpretation of the baffling five per cent which mathematical model in sight with clearly cannot. every step. A d-c motor driven by a d-c genera- tor periodically reverses itself! Jacob P. Den Hartog is Professor A jet engine governor with a Emeritus of Mechanical Engineering centrifugal pendulum vibrates to at MIT. f !P_.&1111111' i

110

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74 75 Nonlinear Vibrations

t3- thyy,7 B The Van der Pol Equation 1,=->o tapes Description of a self-excited system with damping dependent Introduction upon amplitude...reduction of Differences between linear and the differential equation, by nonlinear vibrating systems... dimensional analysis, to its application of various differen- simplest form...comparison of tial equations...physical illus- the Van der Pol number to the trations of some simple syst- Reynolds number. tems...review of literature... description of the phase-plane 31-min. B&W Videotape method of solution. 16-0105 Purchase $210 Rental $21. 36-min. B&W Videotape 16-0101 Purchase $235 Rental $24. Relaxation Oscillations Solutions of the Van der Pol Equation by general phase-plane The Phase-Plane Method Illustrated application of the method..''. determination of limit- amplitude by energy balance... phase-plane method to simple case of large damping (large Van linear systems...undamped vi- der Pol number)... approximate brator...negative spring... calculation of steady state damped vibrator...negative frequency. damping...isoclinics... 'cannibal' asymptotes. 30-min. B&W Videotape 37-min. B&W Videotape 16-0106 Purchase $205 Rental $21. 16-0102 Purchase $240 Rental $24. Periodic Reversal of Rotation of a D.C. Motor Application of the Phase-Plane Presentation of a constant speed Method D.C. series generator driving a Free vibration with'Coulomb separately excited D.C. motor... damping...simple pendulum with explanation of periodic reversal large angular motion...cylindri- of rotation of the D.C. motor on cal phase plane. the basis of the Van der Pol 30-min. B&W Videotape Equation. 16-0103 Purchase $205 Rental $21. 34-min. B&W Videotape 16-0107 Purchase $225 Rental $23. Pendulum in a Rotating Plane Application of phase-plane Forced Undampled Vibrator with method to a simple pendulum Nonlinear Spring rotating about a vertical Solution by means of center line in a vertical Martienssen's method... plane...effect of centrifugal Martienssen's diagram...the force on the oscillation. 'jump phenomenon'...introduction 32-min. B&W Videotape of damping effects by energy 16-0104 Purchase $215 Rental $22. balance...stable and unstable branches in the resonance dia- gram. 33-min. B&W Videotape 16-0108 Purchase $220 Rental $22.

76 75 NONLINEAR VIBRATIONS - Continued

Piece-Wise Linear Systems The Sommerfeld Effect Forced vibration of undamped vi- 'Jump phenomenon' resulting from brator with piece-wise linear a highly damped rotor accel- springs by Martienseen's method erated through its critical' ...systems with clearances and speed by the increase of voltage preset springs. of the driving D.C. motor... 33-min. B&W Videotape idealization of the system and 16-0109 Purchase $220.Rental $22. solution by energy balance. 32-min. B&W Videotape 16-0113 Purchase $215 Rental $22. Forced Vibrator with Nonlinear Damping Replacement of nonlinear damping Tuned Centrifugal Pendulum by 'equivalent' linear damping Frahm's Vibration Absorber as to equalize the work per cycle applied to torsional vibration in each case...reduction to a in reciprocating engines... linear case in which the 'equi- utilization of centrifugal force valent linear damping constant' for required tuning following is dependent on frequency and totational engine speed...(only amplitude. lecture on linear systems). 31-min. B&W Videotape 34-min. B&W Videotape 16-0110 Purchase $210 Rental $21. 16-0114 Purchase $225 Rental $23.

Exact Solutions, (1) Undamped free vibration with non- Nonlinear Centrifugal Pendulum linear spring,.. forced undamped Jump phenomenon observed on air- vibration with piece-wise linear craft piston engine...idealiza- spring...comparison of latter re- tion to a simple system...delib- sult with Martienseen's approxi- erate de-tuning of pendulum for mation in Lesson 9. small angles in order to tune it for large angles of swing... 37-min. B&W Videotape system of two coupled differen- 16-0111 Purchase $240 Rental $24. tial equations, both highly nonlinear. 24 min. B&W Videotape Exact Solutions, (2) Forced vibration with Coulomb 16-0115 Purchase $165 Rental $20. damping...comparison of this exact solution with the approxi- mation of Lesson 10. 35-min. B&W Videotape 16-0112 Purchase $230 Rental $23.

NONLINEAR VIBRATIONS - Complete Set

Videotapes Study Guide Complete set of twenty-three B&W Comments, photographs, reading videotapes assignments, problems, and problem solutions. 244 pp. 16-1100 Purchase $4315 (SAVE $645) (One per student recommended.) 115 DayRental $455 (SAVE 53) 16-2100 Purchase $10.50 each. Suggested Text (10% D±scount on five or more.) Mechanical Vibrations, (Fourth A Complete Self -Study Subject. Edition) by J.P. Den Hartog, McGraw-Hill, 436 pp. The set of videotapes described abozje can be used as a complete self- 16-3100'Purchase $16.50 each. study subject when aocampanied by the Study Guide and Suggested Text.

76 7 7 Solution and Interpretation Method of Galerkin Solution of the preceding equa- Originally proposed for static tions by a modified Martienssen systems...later applied to dy- method giving a diagram from namics and particularly to which the jump phenomenon can be slightly non-linear vibrations seen immediately...calculation ...all previously discussed of the critical angle showing approximate methods shown to be the impossibility of engine special cases of Galerkin. operation with pendulum swing 34-min. B&W Videotape . above 30degrees. 16-0120 Purchase $225 Rental $23. 33-min. B&W Videotape 16-0116 Purchase $220 Rental $22. Applications Treatment of the cubic spring Aircraft Jet Rotor with Ball and the large swing pendulum by Bearings with Clearances the four approximate methods... Reduction of system to a simple comparison of the approximate model...illustration of jump methods with the exact (phase- phenomenon by another modifica- plane) procedure, proving the tion of Martienssen's method... K & B approximation to be the avoidance of large amplitude best of the four. resonances by proper detail 34-min. B&W Videotape dimensioning. 16-0121 Purchase $225 Rental $23.

32-min. B&W Videotape .4110 16-0117 Purchase $215 Rental $22. Modified Martienssen Method- Subharmonic Resonance Method' of Krylov-Bogoliubov Variation of the simple Presentation of systems with Martienssen method adapting it small and moderate nonlineari- to the greater accuracy obtain- ties in the damping or the able bythe K & B or 'harmonic spring...derivation of the balance' method...physical dis- (approximate) result in the cussion of subharmonic resonance. standard manner. 32-min. B&W Videotape 24-min. B&W Videotape 16-0122 Purchase $215 Rental $22. 16-0118 Purchase $165 Rental $20.

Volterra's Fishes Physical Interpretation of the Biological problem of population K & B Formulas fluctuation of two species of Interpretation on the basis of fish dependent upon one another energy balance and Fourier ...dimensionless treatment of analysis of the nonlinear the equations...graphical solu- force...fundamental force har- tion and physical interpretation. monic in phase with motion in- 37-min. B&W Videotape terpreted as a spring; cross- 16-0123 Purchase $240 Rental $24. phase component furnishing dashpot effect. 29-min. B&W Videotape 16-0119 Purchase $195 Rental $20.

78 77 Probability and Random Processes Harry L. Van Trees

Probability is a post-calculus Random Processes is a follow-on approach to this importantmathe- to Probability and a pre- matical discipline. Even a requisite to study in suchareas cursory survey of enijineering, as advanced communications and for example, reveals thewide- queuing theory. Included are spread applicability ofprobabi- discussions of three completely lity theory. Such diverse fields characterized processes- the as systems analysis, decision Poisson, Markov, and Gaussian theory, statistics, automatic processes. control, modern management, and cybernetics all relyon a Harry L. Van Trees is Professor probabilistic approach. of Electrical Engineering at MIT.

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78 rf Probability

Theorem Proving Elementary Probability Theory Introductory lecture on theorem Thirteen 134W lgmm proving. Proof of an "IF and FiZms or Videotapes only IF" type of theorem. Proof by contradiction. Introduction to Probability 18-min. B&W Film or Videotape This lecture presents a few 12-0105 Purchase $125 Rental $20. examples of cases where probabi- lity theory is applied. It discusses the subject of relative frequency and its relationship Probabilistic Models to the idea of probability. Covers the five basic axioms of Physical systems and mathematical probability theory. Illustrates - those axioms through a cumber models. of examples. Shows..that, once 35-min. B&W Film or Videotape probability assignments have 12-0101 Purchase $230 Rental $23. been made which are consistant with the five axioms, the proba- bilistic model of an experiment Formulation of Mathematical is always a legitimate one._ Models (1) Formulation of mathematical models 45-min. B&W Film or Videotape in probability theory. Deals 12-0106 Purchase $285 Rental $29. with the definition of a probabi- listic experiment and with the definition of an event. Three Proof by Induction examples involving the tossing of Continuation of theorem proving. a coin or of dice. Representation Illustrates in detail proof by of events on lines or in two- induction. Presents an example involving the two basic steps of dimensional space. typical proof by induction. 22-min. B&W Film or Videotape 12-0102 Purchase $150 Rental $20. 16-min. B&W Film or Videotape 12-0107 Purchase $115 Rental $20.

Formulation of Mathematical Models (2) Joint Probability Idea of joint probability is Continues discussion of formula- introduced through the use of tion of mathematical models. two examples. Shows that joint Events are defined as a col- probabilities must obey the lection of sample points. The idea of an event in continuous axioms of probability theory. sample space is illustrated. 19-min. B&W Film or Videotape 12-0108 Purchase $130 Rental $20. 30-min B&W Film or Videotape 12-0103 Purchase $205 Rental $21. Conditional Probability (1) First of two lectures on condi- Elementary Set Theory Illustrates Introduces basic ideas of tional probability. elementary set theory,. Defines how probabilities change when events are conditioned by other and illustrates graphically the Definition of condi- ideas of equality, inclusion, events. union, intersection, complementa- tional probability. rity, difference, null-sets, dis- 18-min. B&W Film or Videotape joint sets, and partitioning. 12-0109 Purchase $125 Rental $20. 29-min. B&W Film or Videotape 12-0104 Purchase $195 Rental $20.

79 80 ELEMENTARY PROBABILITY THEORY - Continued

Conditional Probability (2) Product Spaces & Statistically Continuation of the previous Independent Experiments lecture on conditional probability. Extends the concept of statistical The lecture goes through a detailed independence. Construction of example on reliability to illustrate product spaces from statistically the ideas of conditional probability independent experimental, outcomes. Bayes rule is derived. Successive coin tosses. 26-min. B&W Film or Videotape 17-min. B&W Film or Videotape 12-0110 Purchase $175 Rental $20. 12-0113 Purchase $120 Rental $20. Conditional Probability: A Digital Communications Example Conditional probability is il- Random Variables lustrated through a digital Sixteen B&W 16mm comunications example. Cons- Films or Videotapes truction of sample space from conditional probability as- Random Variables ;1) sumptions or measurements. Introduction to random variables. Application of probabilistic Probability distributions and ideas to the design of the probability distribution func- system. tions are defined. Properties of probability distribution 29-min. B&W Film or Videotape fianctions. 12-0111 Purchase $195 Rental $20. 26 -min. B &W Film or Videotape Statistical Independence 12-0201 Purchase $175 Rental $20. The fundamental concept of sta- tistical independence is defined and its meaning is il- Random Variables. (2) lustrated through a number of Continuous random variables. examples. The utility of this Probability densitfunctions concept in probabilistic analysis and their properties. Example is discussed briefly. of a uniform random variable. 19-min. B&W Film or Videotape 20-min. B&W Film or Videotape 12-0112 Purchase $130 Rental $20. 12-0202 Purchase $140 Rental $20.

ELEMENTARY PROBABILITY THEORY - Complete Set Study Guide Films/Videotapes Complete set of thirteen B&W Introduction to the topics, summarization of key concepts, 16 mill films or videotapes. problems, and problem solutions. 12-1100 Purchase $1960 (SAVE $220) 374 pp. (One per student 65 Day Rental $254 (SAVE $19) recommended.) 12-2100 Purchase $12.00 each. Suggested Text (10% Discount on five or more.) Probability and Random Processes, W.B. Davenport, Jr., McGraw Hill, Pretest

1970, 542 pp. ,Mathematics pretest to determine 12-3100 Purchase $19.50 each. profiCiency in calculus concepts and techniques used in Probabi- Lecture Notes lity. 74 pp. Chalkboard photographs of all the 12-5100 Purchase $2.50 each. films/videotapes of Probability. A Complete Self-Study Subject. 12-4100 Purchase $4.50 each. The set of films/videotapes described above can be used as a complete self- study subject when accompanied by the Study Guide, Lecture Notes and Suggested Text.

81 Canonical Random Variables Impulsive Densities Describes the standard variables Densities containing impulses are often used in practice. Expo- discussed. Integration and nential random variable is differentiation for these densities introduced and illustrated. are illustrated. 11-min. B&W Film or Videotape 18-min. B&W Film or Videotape 12-0203 Purchase $80 Rental $20. 12-0208 Purchase $125 Rental $20.

Mixed Random Variables Statistically-Independent Random Random Variables are classified Variables as continuous, discrete or mixed. Statistical independence is The definition of an impulse is defined in terms of probability provided. Detailed example it -- distribution functions. The lustrates mixed random variables. concept is illustrated with the derivation of a marginal density 30"min. B&W Film or Videotape function. The idea of utility is 12-0204 Purchase $205 Rental $21. introduced. 25-min. B&W Film or Videotape Conditioning 12-0209 Purchase $170 Rental $20. The conditioning of random variables is defined. It is shown that conditional random Conditioning by Sets variables have all the proper- The conditioning of probability ties of ordinary random variables. distributions and probability densities on sets is illustrated. 15-min. B&W Film or Videotape Conditional distribution functions 12-0205 Purchase $115 Rental $20. are defined. 16-min. B&W Film or Videotape Multiple Random Variables: 12-0210 Purchase $110 Rental $20. Discrete Definition of joint probability distribution functions. Defini- Point Conditioning tion of marginal probability Conditioning is extended to point- distribution functions. Discus- conditioning. This leads to the sion of the properties of both definition of conditional distribu- A detailed example is presented. tion functions of random variables.

34-min. B&W Film or Videotape 17-min. B&W Film or Videotape 12 -0206 Purchase $225 Rental $23. 12-0211 Purchase $120 Rental $20.

Continous Random Variables Joint probability distribution A Digital Communication functions for continuous random Application variables. Joint probability A detailed example of a com- density functions, marginal munication system with noise distribution functions, and added is presented. Model of marginal density functions for the communication system and the continuous random variables. idea of minimum error decision. Properties and examples. Computation of error probabilities. 34-min. B&W Film or Videotape 49-min. B&W Film or Videotape 12-0207 Purchase $225 Rental $23. 12-0212 Purchase $310 Rental $31.

81 82 RANDOM VARIABLES - Continued

Functions of a Random Variable Computation of probability dis- Statistical Averages tributions for functions of a single random variable. Standard Eleven B&W 16mm procedure for this computation. Films or Videotapes Illustration through example. Statistical Averages: Expectation 22-min. B&W Film or Videotape of a Random Variable 12-0213 Purchase $150 Rental $20. The rundamental concept of expectation is introduced. Com- Functions of Vector Random putation of expected values for Variables (1) continuous and discrete random Computation of probability dis- variables. tributions for functions of 19-min. B&W Film or Videotape vectors of random variables. 12-0301 Purchase $130 Rental $20. Standard procedure. Special case of statistically independent random variables. Expectations of Functions of a 19-min. B&W Film or Videotape Random Variable 12-0214 PUrchase $130 Rental $20. The concept of expectation is extended to functions of random variables. It is shown that Reliability APplications expectation is a ainear operator. Introduction to the computation Examples are presented. of reliability. Standard con- fi uraV.ons of networks. Compo- 23-min. B&W Film or Videotape nts in series and in parallel. 12-0302 Purchase $160 Rental $20. 34 -min. B&W Film or Videotape 12-0215 Purchase $205 Rental $21. Moments of a Random Variable Moments and central moments are Function of Vector Random defined. Variance and standard Variables (2) deviation. Properties of More complicated derivations of variance and examples. probability distributions for functions.of vectors of random 18-min. B&W Film or Videotape 12-0303 Purchase $125 Rental $20. variables. Illustration through example. 11-min. B&W Film or Videotape 12-0216 Purchase $80 Rental $20.

RANDOM VARIABLES - Complete Set Films/Videotapes Study Guide Complete set of sixteen B&W Introduction to the topics, 16 mm films or videotapes. summarization of key concepts, problems, and problem solutions. 12-1200 Purchase $2310,(SAVE $255) 80 Day Rental $308 (SAVE 1) 542 pp. (One per student . recommended.) Suggested Text 12-2200 Purchase $17.50 each. Probability and Random Processes, (10%.Discount on five or more.) W.B. Davenport, Jr., McGraw Hill, 1970, 542 pp. A Complete Self -Study Subject. The set offi.lms/Videotapes described 12-3100 Purchase $19.50 each. above can be used as a complete self- Lecture Notes. study subject when accompanied by theStudY GUideLecture Notes and Chalkboard photographs of all the Suggested Text. films/Videotapes of Probability. 12-4100 Purchase $4.50 each.

82 8t3 The Chebyshev Inequality Joint Moments: Correlation The Chebyshev inequality is Joint moments of random variables derived and explained. The lec- are defined. Correlation, ture also includes a discussion covariance and the correlation of how good a Chebyshev inequality coefficients. Basic properties is as a bound on probabilities. of joint moments. Predictive value. 29-min. B&W Film or Videotape 27-min. B&W Film or Videotape 12-0304 Purchase $195 Rental $20. 12-0308 Purchase $180 Rental $20.

Estimation of Random Variables Linear Estimation Deals with the choice of Linear estimation is introduced. estimators for random variables. Fundamental expressions are The mean-square error is discus- derived. Minimum mean-square , sed as a criterion for estimation. estimators are discussed in this Two examples illustrate the light. concept. 44-min. B&W Film or Videotape 23-min. B&W Film or Videotape 12-0309 Purchase $280 Rental $28. 12-0305 Purchase $160 Rental $20.

Characteristic Functions Conditional Expectation Characteristic functions are The idea of conditional expec- defined. Tile, four fundamental tation is introduced. Conditional properties of characteristic func-. expectation on a joint Gaussian tions are derived. probability density. Importance of the concept in estimation. 25-min. B&W Film or Videotape 12-0310 Purchase $170 Rental $20. 13-min. B&W Film or Videotape 12-0306 Purchase $95 Rental $20. Joint Characteristic Functions Minimum Mean-Square Error The concept of a characteristic Estimation function is extended to vectors of Reviews the idea of the minimum random variables. Properties of mean-square error estimator. An joint characteristic functions are example involving the joint.Gaussian derived and discussed. probability density is presented. 25-min. B&W Film or Videotape 18-min. B&W Film or Videotape 12-0311 Purchase $170 Rental $20. 12-0307 Purchase $125 Rental $20.

STATISTICAL AVERAGES - Complete Set Films/Videotapes Study Guide Complete set of eleven B&W Introduction to the topics, 16 mm films or videotapes. summarization of key concepts, problems, and problem solutions: 12-1300 Purchase $1645.(SAVE $145) 406 pp., 40neqaer student 55 Day Rental $212 (SAVE $16) recommended.) Su1.ested Text 12-2300 Purchase $13.00 each. Pro,ability and Random Processes, (10% Discount on five or more.) W.B.\Davenport, sr., McGraw Bill; 1970) 542 pp. A Complete Self- Study Subject. The set offiTSISiVideOtapes:describe4 12-00 Purchase $19.50 each. above can be used:de a Complete self-, Lecture Notes Study subject when accompanied by the Study Guide, Lecture 'Notes and Chalkboard photographs of all the Suggested Text. films/videotapes of Probability. 12-4100 Purchase $4.50 each.

84 83 Central Limit Theorem Limit Theorems and Statistics The derivation of the central Nine B.Wl&mm limit theorem is outlined. Its FiZr'w or Videotapes. implications are discussed in detail. Illustration approxima- Sample Means and the Weak Law tions through the central limit of Large Numbers theorem. The sample mean is presented as an estimator of expectation. The 35-min. B&W Film or Videotape weak law of large numbers. 12-0404 Purchase $230 Rental $23. Convergence in the Mean-square sense. Discussion of different types of convergence. Introduction to Statistical Inference 30 min. B&W Film or Videotape The idea of statistical inference 12-0401 Purchase $205 Rental $21. is introduced. Estimation of a probability density, estimation of moments, hypothesis testing, Relative Frequency testing with unspecifed alter- Relative frequency.is defined. na tives. The meaning of Shows that the relative frequency statistics. of an event converges to the probability of that event. An 18-min. B&W Film or Videotape example is presented. 12-0405 Purchase $125 Rental $20. 18-min. B&W Film or Videotape 12-0402 Purchase $125 Rental $20. Estimation of the Moments of a Random Variable The Gaussian Approximation Estimation of moments. Unbiased Introduces the idea of using the estimators. Consistant estimators. Normalized variance. Illustration Gaussian approximation for large through the use of two statistical samples. An example using binomial distribution is discus- problems. sed in detail. Comparison 37-min. B&W Film or Videotape between exact estimates and the 12-0406 Purchase $240 Rental $24. Gaussian approximation. 33-min. B&W Film or Videotape 12-0403 Purchase $220 Rental $22.

LIMIT THEOREMS AND STATISTICS - Complete Set

Films/Videotapes Study Guide Complete set of nine B&W Introduction to the topics, 16 mm films or videotapes. summarization of key concepts, problems, and problem solutions. 12-1400 Purchase $1610 (SAVE $140) 254 pp. (One per student 45 Day Rental $184 (SAVE $10) recommended.) Suggested Text 12-2400 Purchase $8.00 each. (10% Discount on five or more.) Probability and Random Processes, W.B. Davenport, Jr., McGraw Hill, 1970, 542 pp. A Complete Self-Study Subject. The set of films/videotapes described 12-3100 Purchase $19.50 each. above can be used as a complete self- study subject when accompanied by Lecture Notes the Study Guide, Lecture Notes and. Chalkboard photographs of all the Suggested Text. . -films/videotapes of Probability. '12-4100 Purchase $4.50 each.

84 Estimation of the Parameter of a Estimation of the Probability Probability Density Density of a Random Variable Procedure and issues in the Detailed example on the estimation estimationof parameters of of a probability density function. probability densities. Like- Pitfalls and procedures for the lihood functions. Maximum like- estimation of probability lihood estimators. Biases. densities. Use of variance analysis. 27-min. B&W Film or Videotape 12-0407 Purchase $180 Rental $20. 36-min. B&W Film or Videotape 12-0409 Purchase $235 Rental $24.

Performance Bounds: The Cramer- Rao Inequality The Cramer-Rao inequality as a lower bound on the variance of unbiased estimators.Efficient estimators. Comments on tne use of efficient estimators. 28-min. B&W Film or Videotape 12-0408 Purchase $190 Rental $20.

85 8( Random Processes

Binary Transmission Wave Introduction Treats the binary transmission Seven B&W wave and introduces stationarity A Videotapes concepts. Introduction to Random Processes 32-min. B&W Videotape Introduces, through the use of 13-0104 Purchase $215 Rental $22. examples, the analytical ap- proaches by 'which random process theory may be applied to a Random Telegraph Wave variety of physical problems. Considers the random telegraph wave and uses that example to 33-min. B&W Videotape introduce the minimum mean- 13-0101 Purchase $220 Rental $22. square error (MMSE) prediction problem. Random Processes: Basic Concepts 24-min. B&W Videotape and Definitions 13-0105 Purchase $165 Rental $20. Extends the usual sample-space definition of random variables Second-Moment Characterizations . to the case of random processes, and thereby introduces the Relaxes the constraint of complete notion of a complete character- characterization by introducing ization. the concept of partial character- ization by the mean function and 28-min. B&W Videotape' correlation function. 13-0102 Purchase $190 Rental $20. 38-min. B&W Videotape 13-0106 Purchase $250 Rental $25. Fixed-Form Random Processes Discusses the simple case of The Role of the Covariance fixed-form processes, wherein Function a small number of random in Estimation variables completely character- Returns to the MMSE prediCtion ize the process. problem for the case in which the predictor is constrained to be 25-min. B&W Videotape linear. 13-0103 Purchase $I70-Rental $20. 22-min. B&W Videotape 13-0107 Purchase $150 Rental $20.

INTRQDUCTION TO RANDOM PROCESSES-CompleteSet

Videotapes Study Guide Complete set of seven B &W A step -by -step path through the videotapes. subject with photoaraphs, problem 13-1100 Purchase $1250 (SAVE $110) sets, quiz, and 'solutions. 35 Day Rental $139 (SAVE $10) 164 pp. (One per student recommended.). Suggested Text 13-2100 Purchase $5.50 each. Probability and Random Processes, (10% Discounton fiveor more.) W.B. Davenport, Jr., McGraw Hill, 1970, 542 pp. A Complete Saif- Study Subject. The set of videotapes described 12-3100 Purchase-$19.50 each. above can be used as a complete self- study subject when acconranieci by the Study Guide and Suggested Text.

86 87 System Classification Linear Systems Provides a further investigation Twelve B&W of the classification of systems Videotapes according to their input-output properties. System Descriptions Introduces the basic concept of a 27-min. B&W Videotape single-input single-output system, 13-0205 Purchase $180 Rental $20. and presents a number of examples and special cases including the Complex Exponential Inputs': important class of linear systems. Frequency Domain Analysis Begins the frequency domain 22-min. B&W Videotape analysis of LTI systems by consi- 13-0201 Purchase $150 Rental $20. dering the response of such systems to complex exponential excitations. Linear System Descriptions 28-min. B&W Videotape Discusses the characterization of a linear time-invariant (LTI) 13-0206 Purchase $190 Rental $20. system in the time domain by its impulse response. Periodic Inputs and Fourier Series 40-min. B&W Videotape Continues the frequency domain 13-0202 Purchase $260 Rental $26. analysis of LTI systems by developing the Fourier series representation for periodic Measurement of Inpulse Response" signals and corisidering the res- Demonstration of the relative ponse of such systems toperiodic invariance of linear time- inputs. invariant system responses to the 28-min. B&W Videotape detailed shape of a pulse input 13 -0207 Purchase $190 Rental $20. of short duration but fixed area. 11-min. B&W Videotape 13-0203 Purchase $80 Rental $20. Fourier Series Demonstration Approximation representation of a square wave by a sum of sine Convolution Integral and cosine waves - even and odd Provides calculational exercises functions, even and odd harmonics, with convolution integrals, i.e. Gibb's phonomenon, mean square the time domain input-output error property. equation for an LTI sytem. 15 min. B&W Videotape 16-min. B&W Videotape 13-0208 Purchase $115 Rental $20. 13-0204 Purchase $115 Rental $20.

LINEAR SYSTEMS - Complete Set

Videotapes Study Guide Complete set of twelve B&W A step-by step path through the videotapes. subject with. photographs,problem sets, quiz, and solutions. 13-1200 Purchase $1970 (SAVE $220) 282 pp. (One per student 60 Day Rental $240 (SAVE $18) recommended.) Suggested Text, 13-2200 Purchase $9.00 each. (10% Discount on five or more.) Probability and Random,Processes, W.B. Davenport, Jr., McGraw Hill, A Complete Self-Study Subject. 1970, 542 pp. The set of videotapes *described 12-3100 Purchase $19.50 each. above can be used as a complete self- study subject when accompanied by the Study Guide and Suggested Text.

87 88 LINEAR sYsrkms - Continued Fourier Transforms Makes the transition from the Second Moment Theory :Fourier series to. the Fourier Eight*B&W transform representation for Videotapes aperiodic signals, and derives the convolution - multiplication Linear Systems with Random theorem that relates the time Process Inputs and frequency domain representa- Begins the study of linear tions of LTI system input-output filtering of random processes by pairs. deriving the mean function and 33-min. B&W Videotape correlation function of the output :13-0209 Purchase $220 Rental $22. of a linear system driven by noise. 31-min. B&W Videotape 13-0301 Purchase $210 Rental $21. System Functions Describes some techniques for measuring system functions Time Averages (impulse response and frequency Builds upon the results of the response), and also considers the previous lecture to investigate analysis of linealE systems the relationship between statistical characterized by differential (ensemble) averages and empirical equations. or the cascade of (time) averages of random processes. several linear systems. 45-min. B&W Videotape 35-min. B&W Videotape 13-0302 Purchase $285 Rental $29. 13-0210 ,Purchase $230 Rental $23.

Frequency Domain Analysis of Fourier Transform Properties Stationary Random Processes Treats the mathematical properties Develops the basic frequency - of the Fourier transform. domain analysis of wide-sense 42-min. a&W Videotape stationary random processes. .13-0211 Purchase $270 Rental $27. 36-min. B&W Videotape* 13-0303 Purchase $235 Rental $24. -Sampling Theorem Discusses the representation of White Noise a bandlimited waveform by its Devoted to the definition and use time samples. of white-noise processes in linear- system calculations. 28-min. B&W Videotape 13-0212 Purchase $190 Rental-$20. 17-min. B&W Videotape 13-0304 Purchase $120 Rental $20.

SECOND MOMENT THEORY - Complete Set

Videotapes Study Guide Complete set of eight B&W A step-dby step path through the videotapes. subject with photographk,roblem 13-1300 Purchase $1590 (SAVE $140) sets, quiz, and solutions. 40 Day Rental $181 (SAVE $10) 230 pp. (One per.student recommended.) Suggested Text 13-2300 Purchase $7.50 each. Probability and Random Processes, (10% Discountph five or more.) W.B. Davenport, Jr., McGraw Hill, 1970,.542 pp. A Complete Self-Stitdy Subject. The set of videotapes described 12-v3100 Purchase $19.50 each- above can be used as a complete self- study subject when accompanied by the Study Guide and Suggested Text.

88 8 9 Two Applications of White-Noise Discusses two applications of Poisson Processes white noise: synthesis of a Five B&W random process with a desired Videotapes spectrum, and measurementOf linear-system impulse response. Introduction to Poisson Processes 18-min. B&W Videotape Introduces the Poisson counting 13-0305 Purchase $125 Rental$20. process through its independent increments property and mentions its potential application areas. Matched Filters 29-min. B&W Videotape Derives the matched-filter as 13-0401 Purchase $195 Rental $20. the optimum linear processor for detection of a known signal in additive white noise. Poisson Counting Processes 41-min. B&W Videotape Reviews the definition of the 13-0306 Purchase $265 Rental $27. Poisson counting process and calculates the counting probabi- lities from its incremental Optimum Fixed Form Linear Filters statistics. Continues the discussion of 40-min. B&W Videotape linear signal processing by considering optimum fixed-form 13-0402 Purchase $260 Rental $26. filters for estimating a random signal embedded in additivee noise. Arrival Times Derives the arrival-time statistics 34-min. B&W Videotape for the Poisson counting process. 13-0307 Purchase $225 Rental.$23. 14-Min. B&W Videotape 13-0403 Purchase $100 Rental $20. Optimum Linear Filters Concludes the discussion of linear signal processing by deriving the Filtered Poisson Process optimum unrealizable filter for Builds upon previous results to estimating a random singal study the statistics of a linearly embedded in additive noise. filtered Poisson impulse train i.e. a shot-noise process. 41-min. B&W Videotape 13-0308 Purchase $265 Rental $27. 30-min. B&W"Videotape 13-0404 Purchase $205 Rental $21.

POISSON PROCESSES - Conyolete Set

Videotapes Study Guide Complete Set of five B&W A step-by-step path through the videotapes. subject wilih photographs problem sets, quiz, and solutions. 13-1400 Purchase $815 (SAVE $70) 118 pP. (One per student 25 Day Rental' $97 (SAVE $10) recommended.) Suggested'Text 13-2400 Purdhase $4.00 each. (10% Discount on five or more.) Probability and Random Processes,' W.B. Davenport, Jr., McGraw Hill, A Complete Self-Study Subject. 1970, 542 pp. The.set of videotapes described 12-3100 Purchase $19:50 each. above can be used as a comptete self- study subject when accompanied by the Study Guide and Suggested Text.

89 9.0 POISSON PROCESSES - Continued

Limiting Behavior of Filtered Finite-State Processes Poisson Processes Discusses explicit solution Continues the development ofshot- techniques for the transient and noise statistics by demonstrating equilibrium behavior of finite the approach of high-densityshot- state Markov processes. noise to a Gaussian distribution. 29-min. B&W Videotape 18-min. B&W Videotape 13-0503 Purchase $195 Rental $20. 13-0405 Purchase $125 Rental$20.

Pure Birth Process Markov Processes Obtains the state-occupation probabilities for a pure-birth Six B&W process. Videotapes 16-min. B&W Videotape Introduction to MarkovProcesses 13-0504 Purchase $115 Rental $20. Begins the study of discrete- state continuous-time Markov processes by use of examples, and Linear Birth Processes introduces the state transition Continues the discussion of the diagram. previous lecture for the case of linear birth processes. 32-min. B&W Videotape 13-0501 Purchase $215 Rental $22. 25-min. B&W Videotape 13-0505 Purchase $170 Rental $20. Markov Process Equations Considers the basic analysis Equilibrium Distributions: techniques for finding the Infinite State Processes transient and equilibriumstatistics Investigates-the existence of of a discrete-state continuous- and solution for the equilibrium time Markov process. distribution in an infinite- state Markov process. 47-min. B&W Videotape 13-0502 Purchase $300 Rental$30. 16-min. B&W Videotape 13-0506 Purchase $115 Rental $20.

5. MARKOV PROCESSES - Complete Set'

Videotapes Study Guide Complete set of six B&W A step-by-step path through the videotapes. subject with photographs, problem 13-1500 Purchase $1020 (SAVE $90) sets, quiz, and solutions. 30 Day Rental $122 (SAVE $10) 156 pp. (One per student recommended.) 13-2500 Purchase $5.00 each. (10% Discount on five or more.)

A CompleftSaP.Stu4 Wrject. The set of videotapes described above can be used as a.complete self- study subject when accompanied by the Stuck Guide.

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91 Gaussian Processes and Linear Gaussian Processes Systems Seven B &W Combines the results of the Videote#)ec previous lecture with'-those of second moment theory to completely Introduction to Gaussian Random characterize the output of a linear Processes system driven by Gaussian noise. Introduces the Gaussian process 11-min. B&W Videotape through examples that make use of 13-0604 Purchase $80 Rental $20. the central limit theorem.' 15-min. B&W Videotape 13-0601 Purchase $115 Rental $20. Gaussian Processes and Nonlinear Systems Uses the moment factoring, pro- Gaussian Random Vectors perty of Gaussian random variables Develops the properties of to investigate the response of Gaussian random vectors including non-linear systems to Gaussian noise. joint probability density, and 17-min. B&W Videotape characteristic functions. 13-0605 Purchase $120 Rental $20. 34-min. B&W Videotape 13-0602 Purchase $225 Rental $23. Linear Optimality and General Optimality Gaussian Random Processes Uses the results of previous Defines the-Gaussian'random lectures in conjunction with the process in terms of Gaussian optimum linear filtering results random vectors and uses the of second moment theory to show definition to show that the mean that linear optimality is identi- and covariance function completly cal to global optimality for dhAradteri2e-:!the,Gaus.s.i4n process. Gaussian processes 17-min. B&W Videotape 31-min. B&W Videotape 13-0603 Purchase $120 Rental$20. 13-0606 Purchase $210 Rent41 $21..

Summary of Gausian Processes Concludes the study of Gaussian processes by summarizing the key properties* derived in the previous lectures. 10-min. B&W Videotape 13-0607 Purchase $75 Rental $20.

GAUSSIAN PROCESSES - Complete Set

Videotapes Study Guide Complete set of seven B&W A step-by-step path through the videotapes. subject with photographs,problem sets, quiz, and solutions. 13-1600 Purchase $870 (SAVE $75), , 180-pp.(One: per student 30 Day Rental $134 (SAVE $10) recommended.) Suggested Text 13 -2600 Purchase $6.00 each (10% Discount on five or more.) Probability and Random Processes, W.B. Davenport, Jr., McGraw Hill, A Complete Self Study Subject. 1970, 542 pp. The set of videotapes described 12-3100 Purchase $19.50 each. above can be used as "a oompiete self- study subject when accompanied by the Study Guide and Suggested Text.

91 Measurement of'Power Density Measurement of Spectra Process Characteristics Provides an introduction to spectral density estimation and Three B&W develops an appreciation for Videotapes the tradeoff between resolution Measurement of Random Process and accuracy. Characteristics 25-min. B&W Videotape Introduces the goals of and 13-0703 Purchase $170 Rental $20. problems encountered in measuring the statistics of a random process from sample- function observations. 32-min. B&W Videotape 13-0701 Purchase $215 Rental $22.

Measurement of Mean-Square Value of a Random Process Evaluates the bias and variance of the time-average estimate of the mean-square value of a Gaussian random process. 41-min. B&W Videotape 13-0702 Purchase $265 Rental $27.

MEASUREMENT OF PROCESS CHARACTERISTICS- Complete Set

Videotapes Study Guide, Complete aet of three B&W A Step.-by.-Step path through the videotapes. subject with photographs, 13-1700 Purchase $600 (SAVE $50) problem sets, quiz,and solutiOns. 15 Day Rental $59 (SAVE $10) solutions.58 pp. (One per student recommended.) r Suggested Text 13-2700 Purchase $4.00 each Probability and Random Processes, J10% Discount Oh five or.more.) W.B. Davenport, Jr., McGraw Hill, 1970 542 pp. A CarpieteSetf-StudlySWVect. Theset of videotapes deemilbect, 12-3100 Purchase $19.50 each. above can be used as a completeeelf stuck subject whenexecontpanied by theStudy Guideand Suggested Text.

92 93 Thermostatics and Thermodynamics Myron Tribus

Thermostatics and Thermodynamics These color videotapes were - An Information Theory Approach recorded in a television studio asks whether there is more than before a small group of practicing an analogy between thermodynamic engineers. The series was pro- entropy and communication entropy. duced in Rochester, New York, What is the connection between under a grant from the Xerox statistical mechanics and thermo- Corporation. dynamics? This series'of ten lectures develops probability Myron Tribus was Senior Vice theory and entropy from an informa- President, Xerox Corporation tion theoretic basis. The results and is now Professor of Engineering are applied to a variety of and Director, Center for Advanced problems to build up the concepts Engineering Study, MIT. of statistical inference needed to establish statistical mechanics and thermodynamics.

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AP- -at/MEM

94 Thermostatics and Thermodynamics

Ten Color Hypothesis Testing and Sequential Videotapes Testing Probability function applied to Entropy in Thermodynamics and Bernoulli trials. The relation Communication between probability and frequency. Constrasts inductive and deductive The evidence form of probability logic. Gives desiderata for the applied to hypothesis testing and design of an inductive logic sequential testing in quality system. Introduces the use of control. Boolean symbols. 49-min. Color Videotape 50-min. Color Videotape 29-0105 Purchase $370 Rental $37. 29-0101 Purchase $375 Rental $38.

Hypothesis Testing Logical Basis for Probability Bayes Equation. The cancer Conditional probability, scaling problem: should a biopsy be rules, functional constraints, the performed? Hypothesis testing. logic of denial statements, allow- The test of a random number able transformations of probability. generator, the Chi Square 49-min. Color Videotape Entropy as a measure of un- 29-0102 Purchase $370 Rental $37. certainty. 49-min. Color Videotape 29-0106 Purchase $370 Rental $37. A System of Inductive Logic Review of consequences of desider- ata for a. system of logic. Pro- Entropy bability as an "encoding" of Entropy as a, measure .of ignorance. knowledge. How to combine Boolean The maximum entropy principle. and ordinary algebraic .operations. An application:predicting order Historic interpretations of pro- size from order data. The Gibbs- bability; Bayes-equation and Jaynes formalismof statistical common sense. inference. 50-min. Color Videotape 51-min. Color Videotape 29-0103 Purchase $375 Rental $38. 29-0107 Purchase $375 Rental $38.

Applying Bayes Equation The Thermodynamics of a Mythical Bayes Equation applied to cancer Economy detection. Calibration vs use of Thermodynamics of Upper and Lower equipment. A method to "extend Slobovia (the "Thermodynamics" of the conversation."Using the a mythical economy). The laws of evidence transformation and other thermodynamics for a non-physical transformations. system. The exponential distribu- 50-min. Color Videotape tion and an analog of temperature. 29-0104 Purchase $375 Rental $38. The concept of negative temper- ature. The grand canonical distribution for an artificial economy. 53-min. Color Videotape 29-0108 Purchase $380 Rental $38.

94 9J Statistical Thermodynamics Statistical Mechanics. The THERMODYNAMICS - Complete Set Boltzrc-n distribution. The grand canonical distribution.. The third Color Videotapes law. The minimum postulates Complete set of ten required for thermophysics. The Color Videotapes relation between macroscopic concepts of work, path, heat, 29-1100 Purchase $3305(SAVE$450) reversibility, etc. and statis- 50 Day Rental $344 (SAVE 34) tical parameters 55-min. Color Videotape 29-0109 Purchase $385 Rental $39.

Classical Thermodynamics Statistical and classical thermo- dynamics compared. The basis for irreversibility in statistical phenomena, the domain of appli- cability of thermostatics. The role of diffusion in entropy generation. Why does thermo- dynamics work? Review of the 10 lectures. 53-min. Color Videotape 29-0110 Purchase $380. Rental $38.

95 90 Special Programs

Among the many lectures and listed for the first time - as demonstrations listed earlier in "Women's Work: Engineering." this catalog are a few that bear special mention. The purpose of In addition,you.will find a this section is to single these special series on "The Management out as well as to introduce a of TechnologiOal Innovation" few one-of-a-kind programs recorded in color in December produced by MIT. Thus, in the 1975. Most of the other.. lectures pages that follow, you will find and demonstrations were recorded listed once again such outstanding in: the CAES color studio; the two demonstrations as "Recursion" as "Women's Work" documentaries, well as such unusual productions - however, were filmed on location.

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96 9! Special Programs

Recursion Visiting Professor Joseph Stoy explains and demonstrates the process of writing recursive programs, i.e. programs that 'invoke themselves. Detailed examples are illustrated (viz. three "monks" working on the Towers of Hanoi puzzle) and worked' out to clarify this frequently misunderstood topic. 40-min. Color Videotape 14-0203 Purchase $330 Rental $33.

Women's Work: Engineering A documentary film designed to motivate young women to consider careers in engineering. Shows women engineering students and professional engineers in school, Vl on the job and at leisure. Also confronts the problem of com- bining a career with the res- ponsibilities of marriage and raising children. 26-min. 16 mm Color Film or Videotape 41 25-0001 Purchase $245 Rental $25. Demonstration of Sampling, Aliasing, and Frequency Response Women's Work: Management Demonstk'ation of sampling and Another in a series of documen- aliasing with a sinusoidal signal. taries encouraging women to Sinusoidal response of a digital consider careers in non-tradi- filter. Dependence of frequency tional fields. Women in various response on sampling period. management roles share their Periodic nature of the frequency experiences, role conflicts, response of a digital filter. aspirations, and satisfactions. Minority women, in particular, 12-min. Color Videotape discuss their unique status in 22-0122 Purchase $120 Rental $20. the management role. 29-min.16 mm Color Eilm or Measurement of Impulse Response Videotape Demonstration of the relative 25-0002 Rental $27 Purchase invariance of linear time- invariant system responses to the detailed shape of a pulse input of short duration but fixed area. 11-min. B&W Videotape 13-0203 Purchase $80 Rental $20.

*Write for purchase price.

97 9 8 SPECIAL PRCX;RAMS - Continued Fourier Series Demonstration Approximation representation of The Management of a square wave by a sum of sine and cosine waves - even and odd Technological Innovation functions, even and odd harmonics, Seven Color Gibb's phenomenon, mean square Videotapes error property. For over a decade, the 15-min B&W Videotape Alfred P. Sloan School of 13-0208 Purchase $115 Rental $20. Management at MIT has carried out a broad research program on the effective management of research and development and on the com- mercial implementation of technological innovations. Six Sloan School faculty members report the status of that re- search in a late 1975 symposium for members of the MIT Industrial Liaison Program.

4 Motivating Scientists and Engineers A Professor Ralph Katz. One of the major issues inevery A Visit with J. Th. G. Overbeek R&D setting. Recent research find- The serious lecturer of the ings and contemporary viewsabout Colloid and Surface Chemistry motivation. Differences from clas- series gives way to the warm sical perspectives and even from human being behind the theories views popular in the '60s. and demonstrations. In an in- ::40-min. Color Videotape terview with John T. Fitch of the 25-0201 Purchase $200. Rental MIT Center for Advanced Engineer- $50. ing Study, Theo Overbeek recounts his life story (beginning with Uses Needs and Industrial his "firm decision" not to be a Innovation teacher!) including the develop- Professor Eric Von Hippel. ment of the D.L.V.O. theory. How to transfer an accurate 30-min. Color Videotape understanding of user need to the 11-0501 Purchase $210 Rental $21. manufacturer. User dominated, manufacturer dominated, and supplier dominated modes. Energy for the Year 2000 :40-min. Color Videotape A 1973 report by four MIT faculty 25-0202 Purchase $200 Rental $50. members interviewed by John Fitch. The factors contributing to the energy crisis, a look at a com- Technical Venture Strategies puter model for predicting the Professor Edward B. Roberts. effects of off-shore drilling, a Entrepreneurial alternatives: visit to a cryogenic generator Investments in small companies, project and a discussion of joint ventures and new venture energy alternatives for the future. spinoffs, and internal venture 29-min. Color Videotape generation. Directions for 25-00C3 Purchase $265 Rental $27. enhancing new venture results. :40-min. Color Videotape 25-0203 Purchase $200 Rental $50.

98 99 Communication in Science and Preparations for Experiments Technology Professor Thomas J. Allen. in Electrophysiology Technical problem-solving oriented communication at the organizational, Dissection of a Frog, Part 1: inter-organizational, and national Sartorius Muscle - J.J. Guinan,Jr. levels. Keeping the organization Demonstrates how to pith a frog abreast of current technology and and how to remove a muscle in a the most effective techniques for way which will make the muscle transferring technology. suitable for intercellular recording. Z40-min. Color Videotape 25-0204 Purchase $200 Rental $50. 14-min. Color Videotape 25-0301 Purchase $140 Rental $20.

Corporate /R&D Interface Management Dr. William H. Gruber.. Dissection of a Frog, Part 2: How performance of corporate /R&D Gastrocnemius Muscle and its divisions is determined by Innervation J.J. Guinan, Jr. management policies and actions Demonstrates how to remove a which affect the interface gastrocnemius muscle and its between R&D and the rest of the innervation, extending from the corporation. A strategy for muscle to the spinal cord. improving performance. 17-min. Color Videotape Z40-min. Color Videotape 25-0302 Purchase $140 Rental $20. 25-0205 Purchase $200 Rental $50.

Dissection of a Frog, Part 3: Sciatic Nerve - J.J. Guinan, Jr. Innovation in Industrial A method for dissecting out the Organizations main nerve trunk from the spinal Profeasor_James Utterback, MIT cord to the ankle. Center for Policy Alternatives and Harvard Business School. 17-min. Color Videotape The changing relationship between 25-0303 Purchase $170 Rental $20. product and production process technologies as a central factor in determining a firm's capabilities Electrophysiology of the Frog for innovation to meet changing Heart - R.G. Mark competitive conditions. Variables Dissection to expose beating heart which can be manipulated by of large pithed frog. Recording corporate management, scientists, of ECG with Ag-AgC1 electrodes. and engineers. Use of suction electrodes to record electrical activity of Z40-min. Color Videotape various portions of heart. Cor- 25-0206 Purchase $200 Rental $50. relation of these signals with observed mechanical behavior and ECG waveforms. MANAGEMENT OF TECHNOLOGICAL 8-min. Color Videotape INNOVATION - Complete Set 25-0304 Purchase $100 Rental $20.

Those renting or purchasing the complete set of six color video- tapes will receive - at no extra, cost - a 40-minute question and answer session with allsix speakers. (Continued on inside back cover.) Seven Color Videotapes 25-1200 Purchase $1200 30-Day Rental $300

99 1 0 0 ORDERING INFORMATION

To order, use the postage-free Formats Order Form on the next page or mail your Purchase Order to: All lectures and demonstrations listed in this catalog are Center for Advanced Engineering available as videocassettes and Study. Room 9-232 videotapes. Many black-and- Massachusetts Institute of white (B&W) programs are also Technology available as l6'.= films. Be Cambridge, Mass. 02139 sure to check the appropriate box in the order form to indicate- Please provide all information the format you want. requested on the Order Form, i.e. zip codes, format desired, catalog numbers, titles, prices, and Delivery dates required. Please reserve films and video- tapes at least two weeks before Note: Don't overlook the special screening date to allow time discounted prices for rentals and for shipment. On complete set purchases of complete sets. rentals, you may wish to sug- gest a screening schedule.

Rentals All shipments will be made by Rental period is five (5) days U.S. Postal Service, pre-paid per film or videotape. For and insured, F.O.B. destination, greater scheduling flexibility, unless otherwise instructed. complete set rentals are recom- Shipment by other carriers are mended because of the longer F.O.B. Cambridge, Massachusetts. rental period. Also note the discounts available when renting complete sets. Restrictions All films, videotapes, and written material in this catalog are copy- Purchases right by MIT and/or others. All Substantial discounts are offered rights reserved. Reproduction for purchases of complete sets. of any part of these materials by Also note that rental fees can be any means is prohibited. The films applied toward purchase price if I and videotapes may not be used on order is received within 30 days television or for paid fees or after rental period. Orders less admissions without the express than $20.00 must be pre-paid. written consent of MIT.

Previews Preview period is three (3) days. Film or tape must be returned immediately thereaftr. Preview films and tapes are.!available only for prospective purchase. Telephone: (617) 253-7444

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