DOCSLIB.ORG

ED164303.Pdf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
ED164303.Pdf DOCUMENT RESUME -.. a ED 164.303 E 025. 458 AUTHOR Beck, A.; And Others ,TITLE Calculus, Part 3,'Studentl'Text, Unit No. 70. Revised Edition. , INSTITUTION Stanford Univ.,'CaliY. School Mathematics Study 't.-Group. SPONS AGENCY -National Science Foundation, Washington, D.C. PUB DATE ,65: NOTE 36bp.; For related documents, see SE 025 456-4:59; Contains light and braken'type EDRS PRICE MF-$0.83 HC-$19.41 Plus Postage. DESCRIPTORS *Calculus; *Cuiriculum; *Instructional Materials; *Mathematical Applications; Mathematics .Educatioi; S4Condary Education; *Secondary School Mathematics; *Textbooks IDENTIFIERS *School Mathematics Study Group ABSTRACT. This is part three of a'three-part SMSG calculuS text for high sahool students. One of the goals of the text is to present -calculus as a mathematical discipline -as yell, as presenting its practical uses. The authbrs emphasize the importance of being able to ipterpret the conceptS and theory interms of models to which they .apply. The text demonstrates the origins of the ideas of the calculus in pradtical problems; attempts to express these ideas precisely and_ ` develop them logically; and finally, returns to the problems and applies the theorems resulting from that development. Chapter topics include: (1)vectors and curves; (2) mechanics; (3) numerical analysis; (4) sequences and series; and (5) geometricl optics and waves. (MP) 1 - ********************************45*******************************/ * Reproductions supplied by EDRS are the best that can' be made ,* + ) - * from the original doCumente ../ * *****************************************************#*****,J U S DEPARTMENT lEDUCATIOPtilmi AI id NATIONALINS1 i I EDUCAT . THiSDOCUMENTHA! DUCEDEXACTLYAS TAE PERSONOR ORGAP ATIkr;T POINTSOF V STATEDDO NOT NECE SENTiOFFifiALNATION EDUCATIONPOSITION Calculus Part 3 Student's Text REVISED EDITION ' The following is a list of all thosewho.participiated in the preparation of this volume: A. Beck Olney High School, Philadelphia, Pa. A. A. Blank . NewYork University, New York, N.Y. 1- F. L. Elder lest Hempstead Jr., Sr. High School, N.Y. C. E. Kerr Dickinson College, Carlisle, Pa. M. S. Klamkin Ford. Scientific Laboratory, Dearborn,MiCh.' /. I. 'Kolodner Carnegie Institute of Technology, -Pittsburgh,Ir--- M. D. Kruskal PrinCeton University, Princeton, N.J. C. W. Leeds, III Berkshire School, Sheffield, Mass. Pa,, M. A. Linton, Jr. William Penn Charter School, Philadelphia, H. M..,,Marston Douglass College, New Brunswick; N.J. Purdue University, Lafayette, Ind. L Marx _ R. Pollack New York Uniyeriiry, New York, N.Y. T. L.Reynolds. College of William and Mary, Williamsburg,Va. R. L Starkey Cubberley High Schoolffalo Alto, Calif. V. Tiversky Sylvania Electronics Defease-La.bs , Mr.Vied, Calif H. Weitzner New York University, New York,gy. Stanford, California Distributed for the School Mathematics Study Group - by A. C. Vroman, 3-67 Pasadena Avenue, Pasadena, California e Financial support for School Mathematics .. Study Group has been provided by the- National Science Foundation. Permission to,make verbatimuse of material in this book must be secured fromthe Director of SMSG. Such'permissiori will be grantedexcept in unusual circumstances. Publications incorporating SMSG materials must include bothan acknowledgment of the SMSG copyright (Yale Universityor Stanford University, as the case may be) anda disclaimer of SMSG endorsement. Exclusive license willnot be granted save in exceptional circumstances,and then only by specific action of the AdvisoryBoard of S 0 1965 by The Board of Trustees of the Leland Stanford Junior University. All rights reserved. Printed in the United States of America. 14, 2' TABLE OF CONTENTS Chapter 11. -VECTORS AND CURVES . 669 11-1. Introduction 669' 11-2. Vector Algebra 672 11-3. Vector Geometry 681 11-4. Products of Two Vectors 690 11-5.7 Vector Calculus and Curves 704 11-6. Curves in the Plare 719. Miscellaneob.s Exercises 743 Chapter 12. MECE=CS - 747% %. 12-1, Intros --fo- 747 12-2.. ElemenTlary Mechanical Problems . , 755 12 -3. Constraints:, Use of Energy Conservation . - 772 12-4. Angular Momentum and Central Forces. ., '790 14iscelleineous Exercises 803, Chapter 13: NUMERICAL ANALYSIS 805 13-1. Introduction . 805 13-2. Iteration 8.08 13-3. Theorem with Remainder 819 13-4. Numerical Integration 829 13 -5. Numerical Solution of First Order Differential Equations 842 Ndscellaneous Exercises . 848 Chapter 14. SEQUENCES AND SERIES . 851 . _ 7 14-1. Introduction . .-. - .. 851. 71-2. Convergence of Sequences . 852 14-3. Series , 863 14-4. Conditional and Absolute Convergence ...873 -,.. 14-5. Parentheses and Rearrangements .ea. .87`( 14-6. Sequences of Functions, Uniform Convergence 883 891 14-7. Power Series I 0 NIscellaneou-s Exercises .., 856 Chanter 15. GEOMZTRICAL OPTICS AND WAVES -901 15-1. Introduction 901 15-2. Gea=atrical Optics 903 15-3. Refraction 927 13-4. Kepler-Lambert, Principle_ 939 15 -5. Huyghents Principle 950 15-6. Periodic Waves, . 959 15-7. Method of Stationary Phase 977 15..78. Mathematical Model for Scattering 1001 1 C law O Chdpter 11 VECTORS AND CURVES . Introduction. 2 Given the curvey = x , we can easily show that the point Awith coordinates (0,0) is at absolute minimum. We also show that the area between the curve and thq liney = x + 2 is 2 (Figure 11-1s). 1. igure 11 rla But suppose we take the figure and rotate it about the point A until the liney = x 2 is horizontal (FigUre 11-1b). As a result of the change yt y Figure 11-lb the point AIs no longer a minimum On the other the area of the . shaded region certainly should not change. This simple example suggests that there are two types of properties associated with curves in the plane-or in space. Certain properties depend on the orientation of the curve with respect to a. set of coordinateaxes, and others do not. In this chapter and the next we shall emphasize thoseproper- . ties which do not depend on the coordinates.You should not suppose that' ,either type of property is more important or more fundamental4Zhan tIle other, for they have different uses.In Section 1-1 to find a box with the largest volume, subject given conditions, we plotted the volume of the-box asa function of the length of-a side (Figure 1-1a).If we were to rotate the reference axes, then the new curve.would be of aittle use'in solving the pro- blem. In, contrast, areas and volutes of regions do_ not depend on the.coordi- nates. For-some problems coordinates are not useful until.the solutiorris almostcomplete; such a pro lem is that of describing themotion of twomutually ( attracting objects. a) We shall introduce new tools particularly appr$riate to the study of.pro- perties independent of coordinate axes.We combine partsof euclidean synthetic, -geometry and the analytic-geometry of De§,car-'-=.s. Synthetic geometry does not employ 'coordin/Ite axes but Is%-very awkward :antitative studies.! Cartesian 670 geometry is an ideal tool for the definition and analysis of curves and sur- races,, but the analysis. rests on the choice of coordinates, even when the re- t / .sults do not. To combine the advantages of both systems we introduce the can- cept of, vector as a translation of.the plane or space,-although later the ce,,n- cept;will be seen to have many other interpretations. We shall devqlop an algebra of vectors with operations corresponding to simple geometric construc- tions. In this way, we can describe space independently of coordinates and yet have the power of algebraic operations. All of this could have been done betor the calculus, but we finally ittroduce a vector calculus, and, bring to bear the f I tools we have developed in earlier chapters. Exercises 11 -1 1. Which of the following quantities are independent of the choice of _ . coordinates? (a) The distance between two points, (b) The distance of -a point from the origin. (c) The angle between two lines. (d) The angle of inclination of,a line: (e) The area of e standard region under the graph y = f(x) . (f) The area bounded by two curves. IL A *5- ,--671 11-2.. Vector Algebra. We shall use the geometricalidea of translationas our primary repreAen- tation of the concept of vector.A vector V is then thoughtof as a mapping of space V : Qonto itself in which all points are translatedthe same distance (the length of7 , written !VD in 'thesame direct:Ion. if rf(P1)= Qi and -1(72)= Q2 It^ then the directed linesegments andP2Q2 have the same length and are parallel (directed line segments are said to be parallel if theynot Figure 11-2a only lie on parallel lines,but also -have the same orientation).We can describe V by the walin which it thal6sjust one point sinceany directed segment -15, where Q = V(P) , defines the direction and ,length of V . It does no harm to picture Vas a flQating directed segment (ofa specified length and direction) which may be attached to an initial pointifconvenient. The interpretation of vectoras a translation clearly makesno use of a coordinate system.Nonetheless, it is often convenientto have a represen- tation of a vector in a given coordinate system. IfV(P1) = QIand y 12` f. X-F 2 Figure 11-215 J We shPll use the word "space"to denote either the Euclidean planeE2 or Euclidean three-dimensional space E3, specifying only when necessary. 1 Cj672 V(P2) = Q2then from the parallelism ofPiQi. and P2Q2 the projections of the two directed segments on any given line are equal in-..length and havethe same orientation. Thus if' P an d P have the x-coordLItes x1 and x 1 2 2 respectively, ' -they. Q1 and Q2 have the x-coordinates x, + and x2 + respect-ively (Figure 1-2b)--.; Here. Itl is the common len..zh of the two pro- jections and t is positive if the projections have the orientation as the x.:axis, and negative if they have the opposite orientation.
Load more

Recommended publications
  • Chapter 1 Geometry of Plane Curves
    Chapter 1 Geometry of Plane Curves Definition 1 A (parametrized) curve in Rn is a piece-wise differentiable func- tion α :(a, b) Rn. If I is any other subset of R, α : I Rn is a curve provided that α→extends to a piece-wise differentiable function→ on some open interval (a, b) I. The trace of a curve α is the set of points α ((a, b)) Rn. ⊃ ⊂ AsubsetS Rn is parametrized by α if and only if there exists set I R ⊂ ⊆ such that α : I Rn is a curve for which α (I)=S. A one-to-one parame- trization α assigns→ and orientation toacurveC thought of as the direction of increasing parameter, i.e., if s<t,the direction of increasing parameter runs from α (s) to α (t) . AsubsetS Rn may be parametrized in many ways. ⊂ Example 2 Consider the circle C : x2 + y2 =1and let ω>0. The curve 2π α : 0, R2 given by ω → ¡ ¤ α(t)=(cosωt, sin ωt) . is a parametrization of C for each choice of ω R. Recall that the velocity and acceleration are respectively given by ∈ α0 (t)=( ω sin ωt, ω cos ωt) − and α00 (t)= ω2 cos 2πωt, ω2 sin 2πωt = ω2α(t). − − − The speed is given by ¡ ¢ 2 2 v(t)= α0(t) = ( ω sin ωt) +(ω cos ωt) = ω. (1.1) k k − q 1 2 CHAPTER 1. GEOMETRY OF PLANE CURVES The various parametrizations obtained by varying ω change the velocity, ac- 2π celeration and speed but have the same trace, i.e., α 0, ω = C for each ω.
    [Show full text]
  • Tangent Lines
    The Kabod Volume 5 Issue 1 Fall 2018 Article 1 September 2018 Tangent Lines Samuel Estep Liberty University, [email protected] Follow this and additional works at: https://digitalcommons.liberty.edu/kabod Part of the Mathematics Commons Recommended Citations MLA: Estep, Samuel "Tangent Lines," The Kabod 5. 1 (2018) Article 1. Liberty University Digital Commons. Web. [xx Month xxxx]. APA: Estep, Samuel (2018) "Tangent Lines" The Kabod 5( 1 (2018)), Article 1. Retrieved from https://digitalcommons.liberty.edu/kabod/vol5/iss1/1 Turabian: Estep, Samuel "Tangent Lines" The Kabod 5 , no. 1 2018 (2018) Accessed [Month x, xxxx]. Liberty University Digital Commons. This Individual Article is brought to you for free and open access by Scholars Crossing. It has been accepted for inclusion in The Kabod by an authorized editor of Scholars Crossing. For more information, please contact [email protected]. Estep: Tangent Lines Tangent Lines Sam Estep 2018-05-06 In [1] Leibniz published the first treatment of the subject of calculus. An English translation can be found in [2]; he says that to find a tangent is to draw a right line, which joins two points of the curve having an infinitely small difference, or the side of an infinite angled polygon produced, which is equivalent to the curve for us. Today, according to [3], a straight line is said to be a tangent line of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c; f(c)) on the curve and has slope f 0(c) where f 0 is the derivative of f.
    [Show full text]
  • March 21–25, 2016
    FORTY-SEVENTH LUNAR AND PLANETARY SCIENCE CONFERENCE PROGRAM OF TECHNICAL SESSIONS MARCH 21–25, 2016 The Woodlands Waterway Marriott Hotel and Convention Center The Woodlands, Texas INSTITUTIONAL SUPPORT Universities Space Research Association Lunar and Planetary Institute National Aeronautics and Space Administration CONFERENCE CO-CHAIRS Stephen Mackwell, Lunar and Planetary Institute Eileen Stansbery, NASA Johnson Space Center PROGRAM COMMITTEE CHAIRS David Draper, NASA Johnson Space Center Walter Kiefer, Lunar and Planetary Institute PROGRAM COMMITTEE P. Doug Archer, NASA Johnson Space Center Nicolas LeCorvec, Lunar and Planetary Institute Katherine Bermingham, University of Maryland Yo Matsubara, Smithsonian Institute Janice Bishop, SETI and NASA Ames Research Center Francis McCubbin, NASA Johnson Space Center Jeremy Boyce, University of California, Los Angeles Andrew Needham, Carnegie Institution of Washington Lisa Danielson, NASA Johnson Space Center Lan-Anh Nguyen, NASA Johnson Space Center Deepak Dhingra, University of Idaho Paul Niles, NASA Johnson Space Center Stephen Elardo, Carnegie Institution of Washington Dorothy Oehler, NASA Johnson Space Center Marc Fries, NASA Johnson Space Center D. Alex Patthoff, Jet Propulsion Laboratory Cyrena Goodrich, Lunar and Planetary Institute Elizabeth Rampe, Aerodyne Industries, Jacobs JETS at John Gruener, NASA Johnson Space Center NASA Johnson Space Center Justin Hagerty, U.S. Geological Survey Carol Raymond, Jet Propulsion Laboratory Lindsay Hays, Jet Propulsion Laboratory Paul Schenk,
    [Show full text]
  • Branches Vol 22
    Branches volume wen y- wo Caldwell Community College and Technical Institute 2855 Hickory Boulevard Hudson, North Carolina 28638 828.726.2200 • 828.297.3811 www.cccti.edu CCC TI is an equal opportunity educator employer Cindy Meissner Untitled Relief Print Acknowledgements Art Editors Laura Aultman Justin Butler Thomas Thielemann Literary Editors Heather Barnett Jessica Chapman DeAnna Chester Brad Prestwood Production Director Ron Wilson Special Thanks: Alison Beard Ron Holste Martin Moore Edward Terry Linda Watts Funding and other support for Branches was provided by the CCC&TI Foundation, the College Transfer Division and the Department of Fine Arts, umanities, Social Sciences, and Physical Education. To view previous editions of Branches or to find out more information about submitting works of art or literature to the 23rd edition of Branches, please visit our website at www.cccti.edu/branches. Table of Contents Factory Reflection ......................................Scott Garnes ................................Frontispiece Sunday Afternoon with Flamenco ..............KJ Maj ..........................................................1 Woman on the Liffey Bridge........................Peter Morris ..................................................3 Void ............................................................Katie Webb....................................................4 Yellow ospital Garments ..........................Mattea Richardson ........................................5 Canned Peaches in Winter ..........................Amy
    [Show full text]
  • Southwestern M O N U M E N
    SOUTHWESTERN MONUMENTS MONTHLY REPORT OCTOBER - - - - 1938 DEPARTMENT OF THE INTERIOR NATIONAL PARK SERVICE SOUTHWESTERN MONUMENTS OCTOBER, 1338, REPORT INDEX OPENING, by Superintendent Frank Pinkley, 27,1 CONDENSED GENERAL REPORT Travel ........... ,277 400 Flora, Fauna, and Natural 000 General. -278 Fhenomena. .280 100 Administrative . , . .278 500 Tse of Facilities by Public,280 200 Maintenance, Improvements, 600 Protection 281 and New Construction . .279 700 Archeology, Fist. ,Pre-Hist... 281 300 Activities Other .Agencies,279 900 Miscellaneous. ...... 282 RETORTS FPOM KEN IN THE FIE'D Arches .£34 Gran Ouivi'-a. ......... .294 Aztec Ruins ......... -.284 Hove:.weep 286 Bandelier .... ...... ..297 Mobile Unit .......... .336 Bandelier CCC ..... .299 Montezuma Jastle. ........ ,305 Bandelier Forestry. , .300 Natural Fridges ........ .320 Canyon de Chelly. ...... .318 • Navajo .312 Capulin Mountain. ...... ,319 pipe Spring 292 Casa Grande .......... -308 Saguaro ............ .237 Casa Grande Side Camp .... .310 Sunset Crater ......... .291 Chaco Canyon. ........ .302 Tumacacori. .......... .312 Chiricahua. ......... .295 -Yalnut Canyon ......... .301 Chiricahua CCC. ....... .296 White Sands .......... .283 El Morrc. .......... .315 Wupatki 289 HEADQUARTERS Aztec Ruins Visitor Statistics.333 Casa Grande Visitor Statistics. .331 Branch of Accounting. .... .339 Comparative Visitor Figures . .329 Branch of Education ..... .324 October Visitors to S.W.M 334 Branch of Maintenance .... :323 Personnel Notes 340 THE SUPPLEMENT Beaver Habitat at Bandelier, By W. B. McDcugall ..... .351 Geology Notes on the Montezuma Castle Region, by E..C. Alberts. .353 Geology Report on the Hovenweep National Monument, by C. N. Gould . .357 Moisture Retention of Cacti,'by David J.'Jones 353 Ruminations, by The Boss. '.'•'. .361 Supplemental Observations, from the- Field ........ .344 , SOUTHWESTERN MONUMENTS PERSONNEL HEADQUARTERS: National Park Service, Coolidge, Arizona. Frank Pinkley, Superintendent; Hugh M.
    [Show full text]
  • Geographic Names
    GEOGRAPHIC NAMES CORRECT ORTHOGRAPHY OF GEOGRAPHIC NAMES ? REVISED TO JANUARY, 1911 WASHINGTON GOVERNMENT PRINTING OFFICE 1911 PREPARED FOR USE IN THE GOVERNMENT PRINTING OFFICE BY THE UNITED STATES GEOGRAPHIC BOARD WASHINGTON, D. C, JANUARY, 1911 ) CORRECT ORTHOGRAPHY OF GEOGRAPHIC NAMES. The following list of geographic names includes all decisions on spelling rendered by the United States Geographic Board to and including December 7, 1910. Adopted forms are shown by bold-face type, rejected forms by italic, and revisions of previous decisions by an asterisk (*). Aalplaus ; see Alplaus. Acoma; township, McLeod County, Minn. Abagadasset; point, Kennebec River, Saga- (Not Aconia.) dahoc County, Me. (Not Abagadusset. AQores ; see Azores. Abatan; river, southwest part of Bohol, Acquasco; see Aquaseo. discharging into Maribojoc Bay. (Not Acquia; see Aquia. Abalan nor Abalon.) Acworth; railroad station and town, Cobb Aberjona; river, IVIiddlesex County, Mass. County, Ga. (Not Ackworth.) (Not Abbajona.) Adam; island, Chesapeake Bay, Dorchester Abino; point, in Canada, near east end of County, Md. (Not Adam's nor Adams.) Lake Erie. (Not Abineau nor Albino.) Adams; creek, Chatham County, Ga. (Not Aboite; railroad station, Allen County, Adams's.) Ind. (Not Aboit.) Adams; township. Warren County, Ind. AJjoo-shehr ; see Bushire. (Not J. Q. Adams.) Abookeer; AhouJcir; see Abukir. Adam's Creek; see Cunningham. Ahou Hamad; see Abu Hamed. Adams Fall; ledge in New Haven Harbor, Fall.) Abram ; creek in Grant and Mineral Coun- Conn. (Not Adam's ties, W. Va. (Not Abraham.) Adel; see Somali. Abram; see Shimmo. Adelina; town, Calvert County, Md. (Not Abruad ; see Riad. Adalina.) Absaroka; range of mountains in and near Aderhold; ferry over Chattahoochee River, Yellowstone National Park.
    [Show full text]
  • All Roads in County (Updated January 2020)
    All Roads Inside Deschutes County ROAD #: 07996 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) <null> <null> 211009 Other Rural Local Dirt-Graded <null> County Road Length: 0 101ST LN ROAD #: 02265 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) 10 0 101ST ST 0.262 END BULB 151204 Deschutes County Rural Local Macadam, Oil 0.262 Mat County Road Length: 0.262 101ST ST ROAD #: 02270 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) 10 0 HWY 126 0.357 MAPLE LN, NW 151204 Deschutes County Rural Local Macadam, Oil 0.357 Mat 20 0.357 MAPLE LN, NW 1.205 95TH ST 151203 Deschutes County Rural Local Macadam, Oil 0.848 Mat County Road Length: 1.205 103RD ST ROAD #: 02259 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) <null> <null> 151209 Local Access Road Rural Local AC <null> <null> <null> 151209 Unknown Rural Local AC <null> 40 2.75 BEGIN 3.004 COYNER AVE, 141228 Deschutes County Rural Local Macadam, Oil 0.254 NW Mat County Road Length: 0.254 105TH CT Page 1 of 975 \\Road\GIS_Proj\ArcGIS_Products\Road Lists\Full List 2020 DCRD Report 1/02/2020 ROAD #: 02261 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) 10 0 QUINCE AVE, NW 0.11 END BUBBLE 151204 Deschutes County Rural Local Macadam, Oil 0.11 Mat County Road Length: 0.11 10TH ST ROAD #: 02188 SEGMENT FROM TO TRS OWNER CLASS SURFACE LENGTH (mi) <null> <null> 151304 City of Redmond City Collector AC <null> <null> <null> 151309 City of Redmond City Local AC <null> <null> <null> 151304 City of Redmond City Collector Macadam, Oil <null> Mat <null> <null> 141333 City of Redmond Rural
    [Show full text]
  • Kapa'a, Waipouli, Olohena, Wailua and Hanamā'ulu Island of Kaua'i
    CULTURAL IMPACT ASSESSMENT FOR THE KAPA‘A RELIEF ROUTE; KAPA‘A, WAIPOULI, OLOHENA, WAILUA AND HANAMĀ‘ULU ISLAND OF KAUA‘I by K. W. Bushnell, B.A. David Shideler, M.A. and Hallett H. Hammatt, PhD. Prepared for Kimura International by Cultural Surveys Hawai‘i, Inc. May 2004 Acknowledgements ACKNOWLEDGMENTS Cultural Surveys Hawai‘i wishes to acknowledge, first and foremost, the kūpuna who willingly took the time to be interviewed and graciously shared their mana‘o: Raymond Aiu, Valentine Ako, George Hiyane, Kehaulani Kekua, Beverly Muraoka, Alice Paik, and Walter (Freckles) Smith Jr. Special thanks also go to several individuals who shared information for the completion of this report including Randy Wichman, Isaac Kaiu, Kemamo Hookano, Aletha Kaohi, LaFrance Kapaka-Arboleda, Sabra Kauka, Linda Moriarty, George Mukai, Jo Prigge, Healani Trembath, Martha Yent, Jiro Yukimura, Joanne Yukimura, and Taka Sokei. Interviews were conducted by Tina Bushnell. Background research was carried out by Tina Bushnell, Dr. Vicki Creed and David Shideler. Acknowledgements also go to Mary Requilman of the Kaua‘i Historical Society and the Bishop Museum Archives staff who were helpful in navigating their respective collections for maps and photographs. Table of Contents TABLE OF CONTENTS I. INTRODUCTION............................................................................................................. 1 A. Scope of Work............................................................................................................ 1 B. Methods......................................................................................................................
    [Show full text]
  • Sources and Studies in the History of Mathematics and Physical Sciences
    Sources and Studies in the History of Mathematics and Physical Sciences Editorial Board J.Z. Buchwald J. Lützen G.J. Toomer Advisory Board P.J. Davis T. Hawkins A.E. Shapiro D. Whiteside Springer Science+Business Media, LLC Sources and Studies in the History of Mathematics and Physical Seiences K. Andersen Brook Taylor's Work on Linear Perspective H.l.M. Bos Redefining Geometrical Exactness: Descartes' Transformation of the Early Modern Concept of Construction 1. Cannon/S. Dostrovsky The Evolution of Dynamics: Vibration Theory from 1687 to 1742 B. ChandIerlW. Magnus The History of Combinatorial Group Theory A.I. Dale AHistory of Inverse Probability: From Thomas Bayes to Karl Pearson, Second Edition A.I. Dale Most Honourable Remembrance: The Life and Work of Thomas Bayes A.I. Dale Pierre-Simon Laplace, Philosophical Essay on Probabilities, Translated from the fifth French edition of 1825, with Notes by the Translator P. Damerow/G. FreudenthallP. McLaugWin/l. Renn Exploring the Limits of Preclassical Mechanics: A Study of Conceptual Development in Early Modem Science: Free Fall and Compounded Motion in the Work of Descartes, Galileo, and Beeckman, Second Edition P.l. Federico Descartes on Polyhedra: A Study of the De Solworum Elementis B.R. Goldstein The Astronomy of Levi ben Gerson (1288-1344) H.H. Goldstine A History of Numerical Analysis from the 16th Through the 19th Century H.H. Goldstine A History of the Calculus of Variations from the 17th Through the 19th Century G. Graßhoff The History of Ptolemy's Star Catalogue A.W. Grootendorst Jan de Witt's Eiementa Curvarum Linearum, über Primus Continued after Index The Arithmetic of Infinitesimals John Wallis 1656 Translated from Latin to English with an Introduction by Jacqueline A.
    [Show full text]
  • Geology and Ore Deposits of the Summitville District San Juan Mountains Colorado
    Geology and Ore Deposits of the Summitville District San Juan Mountains Colorado By THOMAS A. STEVEN and JAMES C. RATTE GEOLOGICAL SURVEY PROFESSIONAL PAPER 343 Prepared in cooperation with the Colorado Metal Mining Fund Board UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1960 UNITED STATES DEPARTMENT OF THE INTERIOR FRED A. SEATON, Secretary GEOLOGICAL SURVEY Thomas B. Nolan, Director The U.S. Geological Survey Library catalog card for this publication appears after page 70. For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price $2 (paper cover) CONTENTS Page Page Abstract_ _______________-------_._- 1 Structure Continued Introduction ___________-__------_-_-- 2 Volcanoes of late Fisher age Continued Acknowledgments__ -. _._---_-__- 3 Younger volcano__--_-._-___----_______-_ 35 Geography..._______-----------__ 3 Faults_ -_____--_-_----_---__________--_-__- 36 History and production__________ 4 Fissures filled by quartz latite dikes_-----__- 36 Previous geologic investigations.__ 7 Early period of fault movement-___--__-_-_ 36 Scope and methods of investigations. 8 Late period of fault movement _____________ 37 Geologic setting._____________________ 9 Altered and mineralized rocks--____________________ 37 10 Rocks altered during Conejos time_-_------_---_ 38 Rock classification and nomenclature__--.-_------- 10 Rocks altered during Fisher time._______-__---_ 38 Conejos formation ___________._______L.______-__ 11 Limits and scope of alteration study. ______i 39 Lithology.___________________-_----_-___-__ 11 Structural setting.________________________ 40 Petrography ____ ________-__------_-_-__ 12 Description of altered rocks._--__________-_ 40 Chemical composition_-_______----_---_-_-_- 13 Quartz-alunite zone._--______-______-_ 41 Fisher quartz latite_______________-_ _---_------- 13 Distribution of rock types.____-_-.
    [Show full text]
  • Lunar Surface Mechanical Properties
    JOURNALOF GEOrItYSICAL RESEARCIt VOL. 73, NO. 22, NOV•-a•B•.R15, 1968 Lunar Surface Mechanical Properties E. M. CHRISTENSEN,1 S. A. BATTERSON,2 H. E. BENSON,3 R. CHOATE,1 R. E. HUTTON,4 L. D. JAFFE,1 R. H. JONES,5 H. Y. No,6 F. N. SCHMIDT,7 R. F. SCOTT,8 R. L. SPENCER,1 AND G. H. SUTTON9 The surfacematerial at the Surveyor5 site is granular and slightly cohesive.Spacecraft footpadsplowed trenchesin this material as the spacecraftslid during landing.For a com- pressiblesoil model, a static bearing capacity of 2.7 newtons/cm•' gave best agreementwith the observations. Static firing of the vernier engines against the surface moved surface particles; a crater 20 cm in diameterand about 1 cm deep was produced,apparently at engine shutdown.The permeability of the soil to gases,to a depth of about 25 cm, is 1 X 10-s cm.ø, correspondingto soil particles mostly 2 to 60 t• in diameter. SPACECRAFTLANDING angular positions, one accelerometerreading, Description. The basic configuration and and three vernier engine thrust commands. landing mechanismfor Surveyor 5 were essen- 2. Analog signals monitoring three strain- tially the same as for Surveyors 1 and 3. Dur- gage bridges, one on each landing leg shock ing the landing, the three landing legs rotate absorber,indicating its axial loading. upward against the resistance of the shock 3. Post-landing television camera coverage absorbers. Following the initial impact, the of footpads,crushable blocks, and areas on the shock absorbers re-extend, returning the legs lunar surface in which these spacecraft mem- bers contacted the surface and came to rest.
    [Show full text]
  • Communications of the LUNAR and PLANETARY LABORATORY
    Communications of the LUNAR AND PLANETARY LABORATORY Number 70 Volume 5 Part 1 THE UNIVERSITY OF ARIZONA 1966 Communications of the Lunar and Planetary Laboratory These Communications contain the shorter publications and reports by the staff of the Lunar and Planetary Laboratory. They may be either original contributions, reprints of articles published in professional journals, preliminary reports, or announcements. Tabular material too bulky or specialized for regular journals is included if future use of such material appears to warrant it. The Communications are issued as separate numbers, but they are paged and indexed by volumes. The Communications are mailed to observatories and to laboratories known to be engaged in planetary, interplanetary or geophysical research in exchange for their reports and publica- tions. The University of Arizona Press can supply at cost copies to other libraries and interested persons. The University of Arizona GERARD P. KUIPER, Director Tucson, Arizona Lunar and Planetary Laboratory Published with the support of the National Aeronautics and Space Administration Library of Congress Catalog Number 62-63619 NO. 70 THE SYSTEM OF LUNAR CRATERS, QUADRANT IV by D. W. G. ARTHUR, RUTH H. PELLICORI, AND C. A. WOOD May25,1966 , ABSTRACT The designation, diameter, position, central peak information, and state of completeness are listed for each discernible crater with a diameter exceeding 3.5 km in the fourth lunar quadrant. The catalog contains about 8,000 items and is illustrated by a map in 11 sections. hiS Communication is the fourth and final part of listed in the catalog nor shown in the accompanying e System of Lunar Craters, which is a_calalag maps.
    [Show full text]