Math 242 Mathematics for Engineering and the Sciences III

SECTION: 004 QUARTER: Spring 2009 (11:00 – 12:15) CLASSROOM: GTM 303

INSTRUCTOR: Dr. Brian Barron OFFICE NUMBER: GTM 348 PHONE: TECH 2453

OFFICE HOURS: MWF (8:00 – 9:30); TR (10:00 – 2:00) EMAIL: [email protected] WEB: www.latech.edu/~bbarron

PREREQUISITE: Math 241 COREQUISITES: PHYS 201 and ENGR 122

COURSE GOALS: To investigate topics in integration of single variable functions, approximations, and introductory probability and statistics.

TEXTBOOKS: Calculus—Early Transcendentals (6th Ed.), 2008 Thomson Brooks/Cole, by James Stewart, and Single Variable Calculus with Precalculus (2nd Ed.) by B. Schröder

COURSE OUTLINE: To be covered are: Stewart 4.8, 5.5, 6.1-6.4, 7.1-7.8, and 8.3, and Schröder 4.3, 15.5, 16.1, 17.1-17.6, and 18.1-18.3.

ATTENDANCE REGULATIONS: Class attendance is regarded as an obligation as well as a privilege. All students are expected to attend regularly and punctually; failure to do so may jeopardize a student's scholastic standing and may lead to suspension from the university. For additional requirements see the University Bulletin.

HOMEWORK POLICY: Homework will be completed using WeBWorK (http://webwork.latech.edu/ ). Additional suggested study problems from the text will be posted on Blackboard. WeBWorK will contribute 30 points to the overall grade. WeBWorK assignments will be graded based upon what is completed online – paper submissions will not be accepted.

SPECIAL PROJECT: There will be a special project during the term. The project will count for 20 points of the overall grade.

CALCULATOR/COMPUTER POLICY: Calculators with symbolic capabilities generally will not be allowed on tests unless the instructor expressly makes an exception. Access to Mathcad and/or Excel may be required for the course.

EXAMINATIONS: Three tests and a comprehensive final examination will be given. Short written assignments and/or projects (variable number of points each) may also be given. Points may also be awarded for completion of WeBWorK assignments. NO CELL PHONES, PAGERS, PDAs, CD PLAYERS, RADIOS, OR OTHER SUCH DEVICES MAY BE USED DURING ANY TEST OR EXAM.

GRADE DETERMINATION PROCEDURE: A grading scale with the usual ten point cut-offs will be used: A=90%-100%, B=80%-89%, C=70%-79%, D=60%-69%, F=59% and below. Your grade will be computed by dividing the total number of points you earn (tests, exams, written assignments, projects) by the total number of possible points. Points will be determined as follows: Exams (3x100) = 300 points; Webwork: 30 points; Project: 20 points; Final: 150 points TOTAL: 500 points

EXAMS MISSED: For EXCUSED absences, the instructor may (at his or her discretion) allow a makeup test or replace the missed test grade by the grade from the final exam.

STUDENTS NEEDING SPECIAL ACCOMMODATIONS & RETENTION OF GRADED MATERIALS: Students needing testing accommodations or classroom accommodations based on a disability are encouraged to discuss the need with me as soon as possible. In the event of a question regarding an exam grade or final grade, it will be the responsibility of the student to retain and present graded materials which have been returned for student possession during the quarter.

HONOR CODE AND ACADEMIC MISCONDUCT: Honor Code Statement “Being a student of a higher standard, I pledge to embody the principles of academic integrity.” For details on the honor code, please refer to: http://www.latech.edu/documents/honor-code.pdf .

NOTE: This class is a part of the MATH 240 series and the Cumulative Mathematics GPA Policy for engineering programs. If you are an engineering major, please read the policy at http://www.latech.edu/coes/assets/engr_math_policy.pdf and see your program's curriculum check sheet for more details."

MATH 242 Outline

Day Book-page Section Suggested Assignment 1 Stew 406 5.5 The Substitution Rule 1-65, every other odd 2 Stew 420 6.1 Areas between Curves 1,3,5,7,13,21,27,45 3 Stew 430 6.2 Volumes 1,3,5,9,13,19,31,53 4 Stew 436 6.3 Volumes by Cylindrical Shells 3,5,9,11,15,19,21,25 5 Stew 441 6.4 Work 1,7,13,15,21 6 Stew 445 6.5 Average Value of a Function (Optional, if time) 1,3,5,9,19 7 Stew 457 7.1 Integration by Parts 3,7,9,13,21,25,33,51 8 Stew 465 7.2 Trigonometric Integrals 1-61, every other odd 9 Stew 472 7.3 Trigonometric Substitution 1,3,7,15,19,23 10 Test 1 (Sections 5.5, 6.1-6.5, 7.1-7.2) 11 Schröder 135 Schröder 4.3: Systems of Linear Equations 1a,d,f,g,h,n, 2a, 3a,b, 5,6 12 Stew 481 7.4 Integration of Rat. Functions by Partial Fractions 1,3,5,7,11,13,17,25,29,35,39,45,53 13 Stew 488 7.5 Strategy for Integration 1-77, every other odd Stew 491 7.6 Integration Using Tables and CAS 1,9,11,21,23, 39 14 Stew 515 7.8 Improper Integrals 1-41, every other odd, 49,57,67,71 15 Stew 505 7.7 Approximate Integration 1,3,5,7,15,19,29,33 16 Schröder 527 16.1 Higher Order Approximations (Taylor Polynomials) 1a,c,e,g, 2a,c,f,j, 3a,c, 4a,c, 5a,c (mention linear approximation, also) 17 Stew 338 4.8 Newton’s Method 1,5,9,11,13,15,27,29,37 18 Schröder 553 17.1 (formerly DST.1), Fundamentals on Probability 17.1: 1a,b,c, 2a,b, 4a,b, 5a,b,c, 6a Function 19 Test 2 (Sections 7.3-7.8, 16.1, 4.8) 20 Schröder 557 17.2 (formerly DST.2), Continuous Random Variables 17.2: 2, 3, 4a,c,d,j, 5, 6 Schröder 565 17.3 (formerly DST.3), Some Widely Used Density 17.3: 1, 2, 5, 6, 8, 10 Functions 21 Schröder 565 17.3 (formerly DST.3), Some Widely Used Density 17.3: 13, 17, 18, 20, 21, 23, 27 Functions 22 Schröder 569 17.4 (formerly DST.4), Cumulative Distribution Functions 17.4: 1, 2, 3, 5, 6, 9, 11, 13, 14 23 Stew 547 8.3 Applications to Physics and Engineering 1,3,19,23,27,29 24 Schröder 515 15.5 (formerly API.5): Centers of Mass of Linear Densities 15.5: 1a,b,c, 3a,b (Optional: RSM (Engr 220 text) 5.7: 5-89 ) 25 Schröder 575 17.5 (formerly DST.5), Mean and Variance 17.5: 2, 3d,h,i, 5a, 6, 7 26 Schröder 578 17.6 (formerly DST.6), Questions to Ask When Solving 17.6: 1, 2, 3, 4, 6, 9 Statistics Problems Schröder 582 18.1 (formerly SAM.1), Some Sample Statistics 18.1: 1, 4 Schröder 589 18.2 (formerly SAM.2 or SAM.3 in older printings) 18.2: 1, 2, 5, 9 Statistical Behavior of the Sample Mean (only large samples) 27 Schröder 589 18.2 (formerly SAM.2 or SAM.3 in older printings) 18.2: 8, 10, 11, 13, 17, 21 Statistical Behavior of the Sample Mean (only large samples) 28 Test 3 (Chapters 17 and 18 and Sections 8.3 and 15.5) 29 Schröder 596 18.3 (formerly SAM.3 of SAM.6 in older printings) 18.3: 2, 3, 4, 5 Confidence Intervals 30 Final Exam

A Note to the Instructor:

The above syllabus and outline represent some of the modifications made to Math 242 in the Math 24x course revisions during the Fall Quarter 2008. In particular, the block of sections on ordinary differential equations (and also exponential growth and decay) has been removed and replaced by the block of sections on probability and statistics from Math 243. These changes are effective for the Winter Quarter, 2008-2009. Additional changes effective for Spring Quarter 2009 include: (1) deleting sections 5.1-5.4 (Areas and Distances, The Definite Integral, FTC, Indefinite Integrals) of Stewart which have been moved to Math 241, (2) separating sections 6.4 (Work) and 6.5 (Average Value of a Function) in Stewart leaving a day for each (though 6.5 is still optional depending on the time available), (3) moving section 7.7 (Approximate Integration) back a couple of days and putting it into an “approximation block” with section 16.1 (Taylor Polynomials and a mention of the linear approximation) from Schröder and section 4.8 (Newton’s Method) from Stewart. (4) moving section 8.3 (Applications to Physics and Engineering) to the stat sections for grouping with linear densities.

Note that section 4.3 (Systems of Linear Equations) from Schröder continues on the syllabus for the time being. It is planned to delete this section after the new Linear Systems & Matrices block in 240 has had its effect.

The syllabus and outline are provided for your guidance only. While we should strive to cover the sections indicated, feel free to make modifications as you see fit.

In Particular:

How many tests you give is up to you (within reason of course. Thirty tests will be too many. One or two in a class like this is not nearly enough.). The tests do not have to be of equal weight. They do not all have to count the same number of points. However, the less eccentric your grading system is, the less likely you are to have to deal with “But I thought I was passing…”

Which homework problems you assign is up to you. You may wish to assign more problems (or fewer) or provide an extra emphasis on problems of certain types. The problems listed above are chosen with an eye towards providing appropriate practice and drill as well as conceptual enlightenment.

Whether you choose to grade homework problems (or have them graded) as part of the student’s class grade is up to you. Keep in mind, however, that work which is not done in your presence may not be done by the person whose name is on the paper. For this reason, current thinking is that the homework grade should not be the dominant part of the course grade. WeBWorK has also been used successfully as a graded homework component which avoids (potentially) many of the problems with traditional homework assignments.

You may also wish to include individual or group projects or reports as part of your grade, again with the caveat that they should not comprise the dominant part of the course grade.

The only sections that “really” need a calculator or MathCad or Excel are 7.6 (integration by CAS), 7.7 (numerical integration), and 4.8 (Newton’s method). However, the inclusion of the probability and statistics material from Math 243 means that a lot of decimal arithmetic will have to be performed by hand if no calculators are allowed at all. Additionally, some instructors might want to have students find values of the normal distribution using numerical integration on calculators instead of doing table lookups. Whatever your calculator policy is, we are still trying to avoid the situation in which students are taking tests on symbolic integration using calculators that will do symbolic integration.

We occasionally do get an EMS worker in class, so possible exceptions to the “no cell phone/pager/etc.” rule exist.

The day by day outline is set up for an MWF class schedule and a standard thirty day quarter. If the class meets on TR, the schedule will have to be modified by doing a lesson and a half per day, on average.

If you have questions about conducting the course, find a faculty member who looks like he or she might know and ask them something. Feel free not to accept the advice.