Bryn Mawr College, Fall 2002
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Professor: Kris Tapp Office: Park Science Building #360 Phone: (610) 526-7483 |
Lectures: MWF 11:10-12 in Park 338 Office hours: M 1-3, W1:30-3 or appointment Email: ktapp@brynmawr.edu |
Text: This course covers chapters 13-17 of Multivariable Calculus, 4th edition, by Stewart. There is a short version of the book that contains only chapters 13-17, and there is a long version that contains chapters 1-12 (one-variable calculus) as well.
Prerequisites: Before enrolling in this course, you should have taken the equivalent of two semesters of calculus. In particular, you should know how to
· Graph, differentiate, and integrate common functions of one variable (including exponential, logarithmic, and trigonometric functions).
· Optimize a function of one variable (find max and min).
· Integrate by parts and by substitution.
· Use the 2nd derivative test to classify a critical point as a max or a min.
Goals of the course: Our main object of study is a function of two or more variables. We will apply tools of calculus that you know (differentiation and integration) to study such functions, and also develop new tools. I will emphasize conceptual understanding and real world applications, as well as algebraic skills.
Homework: Homework will be posted to the course web page every week. It is due on Wednesday of the following week. If you need an extension on homework, please speak with me before or on the Wednesday when it is due. I recommend working on homework in small groups, but please write the solutions in your own words.
Exams: We will have two midterm exams and a self-scheduled final exam. The midterm exams may be take-home or at least have a take-home portion (we can decide this together later). Exams may not be taken late without advanced permission. Extensions are usually granted ONLY for family emergencies, infirmary or hospital stays, or similar major crises.
Computer Labs: There will be 6 evening computer labs (listed on the syllabus below) which you must attend this semester. Each lab is scheduled for 2 hours, although many do not take that long. You will have your choice of several times to attend lab (sign-up will happen the second week of class). In lab, you might work with students from the other two sections of Multivariable Calculus.
Help sessions: Lisa Marchisio will run help sessions, in which you can get assistance with homework problems and course ideas. These sessions will be held every MON, TUES and WEDS from 7-9pm in room 338 of Park Science Building.
Final Project: As a culmination of your computer lab work, you will do a project that will be presented during a combined poster session-pizza party at the end of the semester. For this project, you many choose a problem from a list (to be distributed shortly), or you may invent your own project relating multivariable calculus to a real world phenomenon of interest to you.
Disability accommodations: Students who think they
may need accommodations in this course because of the impact of a disability
are encouraged to meet with me privately early in the semester. Students should also contact Stephanie bell,
Coordinator or Accessibility Services, at 610-526-7351 in Canwyll House, as
soon as possible, to verify their eligibility for reasonable
accommodations. Early contact will help
avoid unnecessary inconvenience or delays.
Course grade: Your course grade is the weighted average of the following grades:
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HW 15% Labs 10% Final project 10% |
Midterm 1 20% Midterm 2 20% Final Exam 25% |
Tentative Syllabus
|
Week |
Topics |
Assignments |
|
9/2 |
·
Introduce Course,
13.1 -- 3D coordinates,
13.2 Vectors,
(Prove Pythagorean Theorem
& 3D distance formula) ·
13.3 Dot product ·
13.4 Cross product |
13.1 # 3,4,5,10,11,41 13.2 # 4,5,18,25,33 13.3 # 2,5,7,14,19,39,41 13.4 # 1,2,10,15,29,45 + Wave extra credit problem (Due 9/11) |
|
9/9 |
·
13.5 Lines and planes ·
13.7 Spherical coordinates ·
Catch up & review chapter 13 |
13.5 # 2,11,17,19,22,24,27,31,36,46 13.7 # 3,9,13,17,19,20,31-36,37,39 (Due 9/18) |
|
9/16 |
·
14.1 Space curves ·
14.2 Derivative of space curve (skip integrals) ·
14.3 Arc length and curvature <Computer Lab #1> |
14.1 # 7-12,16,18,21,22 14.2 # 3,4,6,23,49,50 14.3 # 1,2,7,16,25,27 14.4 # 3,5,7,16,21 (Due 9/25) |
|
9/23 |
·
14.4 Velocity and acceleration ·
15.1 Functions of several variables (computer demos) ·
Catch up & preview partial
derivatives <Computer Lab #2> |
15.1 # 1,3,5,6,7,23-30,34,35,36,39,40,51-56 15.3 # 1,2,6 (Due 10/2) |
|
9/30 |
·
15.3 1st & 2nd order partial
derivatives ·
15.4 Tangent planes & linear approximations |
15.3 # 5,12,13,15,17 (Due 10/9) |
|
10/7 |
·
Review for midterm (Mon 10/7) · Take midterm #1 (Wed 10/9) ·
Special topics (Fri 10/11) |
15.3 # 45,49,51,63,64 15.4 # 1,2,19,20,22 (Due 10/23) |
FALL BREAK week of 10/14 |
||
|
10/21 |
·
15.5 Chain Rule · 15.6 The gradient and directional derivatives |
15.5 # 13,14,15,33,35,36,40 15.6 # 1,7,8,10,21,24,27,36 (Due 10/30) |
|
10/28 |
· 15.7 Max/Min values · 15.8 Lagrange Multipliers <Computer
Lab #4> |
15.7 # 3,4,28,31,41,49 15.8 # 1,3,18,23,29,37 (Due 11/6) |
|
11/4 |
· 16.1 Double integrals · 16.2 Iterated integrals · 16.3 Double integrals over general regions <Computer Lab #5> |
No homework. |
|
11/11 |
·
Review for Mid2 (Mon 11/11) · Take Midterm 2 (Wed 11/13) · Special topics (Friday 11/15) |
16.1 # 6,9 16.2 # 13,22,23,24,33 16.3 # 1,7,15,19,33,39 (Due 11/20) |
|
11/18 |
·
16.4 Double integrals in polar coordinates ·
16.6 Surface area ·
16.9 Change of variables in double integrals (skip triple) ·
17.1 Vector fields <Computer Lab #6> |
16.4 # 8,9,24,27,31,32 16.6 # 6,9 16.9 # 1,7,10,13,23 (Due 12/2) |
|
11/25 |
·
Catch-up
-----Thanksgiving Break----- |
|
|
12/2 |
·
17.2 Line integrals ·
17.3 Fundamental Theorem for line integrals |
FINAL HOMEWORK ASSIGNMENT: 17.1 # 1,3,5,21,26,29-32 17.2 # 1,6,7,18,19,43 17.3 # 1,3-6,11,23 17.4 # 1,2,18,19,20 (for 19 & 20, set up but do not solve
the integral) DUE 12/13 |
|
12/9 |
·
17.4 Greens Theorem ·
Special Topics ·
Review for final exam |
|
|
Comprehensive self-scheduled final exam |
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