Calculus III (MATH V1201-006, Fall 2006)


[ Policies & Procedures | Schedule of Lectures ]

Day & Time: Monday and Wednesday 1:10 — 2:25pm

Location: 312 Math

Instructor: Joël Bellaïche

Office Hours (Please note the change): Tuesday 2:30pm-3:30pm and Friday 11:30am-12:30pm

Teaching assistants : Allison Knupp (undergraduate TA) and Wei Zhang

Textbook: James Stewart, Calculus: early transcendentals fifth edition, Brooks/Cole-Thomson Learning, Belmont, CA, 2003. ISBN 0534393217. It is available at the University bookstore or AddALL.

Prerequisites: Calculus I or the equivalent.

Examinations: There will be two in class tests. The first will be on Wednesday, October 11 and the second on Monday, November 13. The final exam is scheduled on Monday, December 18, 1:10-4pm

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Policies & Procedures

Goals: At the end of the course, students should be able to

Expectations: To achieve these goals, students are expected to

Assessment: The course grades will be computed as follows:
20% Homework
20% First test
20% Second test
40% Final exam

Tests and Exams: There are no makeups for missed tests. You must take the final examination at the time scheduled by the university; no final exams will be given earlier.

Homework: There will be two kinds of homework:

Written work: We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit; an assertion is not an answer. For specific suggestions see A guide to writing in mathematics classes.

Academic honesty: It is the obligation of each student to understand the University's policies regarding academic honesty and to uphold these standards. Students are encouraged to talk about the problems, but should write up the solutions individually. Students should acknowledge the assistance of any book, software, student or professor.

Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. You may also take advantage of the Mathematics Help Room (333 Milbank Hall, on the Barnard campus). You may drop by whenever the Help Room is open; no appointment is necessary.

Calculators: Calculators — in particular graphing calculators — are not required for this course. If you have one, you are welcome to use it when you do your homework. However, calculators will not be allowed during any tests or exams.

Disabilities: Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, stop by the Office of Disability Services (BC, CC) to register for support services.

Extra Credit: A maximum of 3 points (added to your average grade, over 100, for the course) is available for extra credit. To earn those 4 points, you should completely solve exercises 4 and 5 page 885, carefully explain your reasoning, and put them into my mailbox before December 12th, 2pm.


Schedule of Lectures

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Class Topic Read   Exercises Due
Sep 06 Vectors §12.2 p.805: 3,4,5,6,18,21,22; p.806: 31
Sep 11 Vectors and their coordinates §12.1 p.797: 5,8,15,16,35,36
Sep 13 Dot product §12.3 p.813: 23,27,43,46,49,51; p.814: 56,58,59
Sep 18 Cross product § 12.4 Problems set 1
Sep 20 Coordinates of points ; equations of spheres and planes §12.1,12.5 p.797: 4,11,14,19,25,30; p.830: 23,26,29,42 Problems set 2 Solutions
Sep 25 Equations of lines; Polar coordinates §12.5,10.3 p.830: 6,17,19,57,62; p.677: 7,13,14,15,16,21,27
Sep 27 Complex numbers. Exponential function. App. G p. A56: 1,2,5,7,9,11,13,15,19,20,23,27,33,35,41 to 44 problem set 3 Solutions
Oct 02 Complex exponential. Cylindrical coordinates. App. G, §12.7 p.843: 9,10,12,57,58,63
Oct 04 Spherical coordinates. Vector functions. §12.7,13.1 p.843: 19,23,28,32,33,34,35,37,47; p.855: 1,2,3,4,5,6 problem set 4
Oct 09 Vector functions. Short review. §13.1 Review, p.844-846 : Concept Chech : 1 to 12, True-False Quiz, exercise 1,2,3,4,5,7,8,9,11,12,13,15,17,19,26,27,37,47
Oct 11 Midterm I : (Solutions) Training Midterm Solutions(new) Problems set 5
Oct 16 Vector functions and space curves §13.1 p.855: 1,2,3,15,19-24, and this
Oct 18 Derivative of vector functions §13.2 p.861: 3,4,5,6,8,9,12,15
Oct 23 Integral of vector functions; Arc length. §13.2,13.3 p, 869: 1,2,3,4,5,6 Problems set 6
Oct 25 Curvature §13.3 p.869: 7,9,10,12,21,23,24
Oct 30 Osculating circle. Velocity and acceleration §13.3,13.4 p. 869: 39p; p.870: 26,27,32,47,49,50
Nov 1 The tangential and normal components of acceleration §13.4 p.879: 3,4,9,10,15,16,19,23,24,31,32,33,39,40 Double problems set 7 and 8
Nov 6 University holiday
Nov 8 Review. Function of several variables Chapter 13. §14.1
Nov 13 Midterm 2 (Solutions) Chapter 13 training exercises Solutions
Nov 15 Functions of several variables. Limits and continuity. §14.1,14.2 p.898-899: 6,7,11,12,13,15,19,21,22,23,24,35,36,39,40,41; p.908-909 : 5,6,7,8,9,14,17,19
Nov 20 Partial derivatives. Tangent Planes. Linear approximations. §14.3,14.4 p.920: 11,12,17,18,19; p.921: 57,58,66; p.930: 27,28,29,36,37
Nov 22 The chain rule §14.5,14.6 p.938: 1,2,3,4,21,22,23,27,28,35,36 Problems set 9
Nov 27 Directional derivatives. §14.6 p.951: 7,8,9,11,12,13,21,22,27,32
Nov 29 The gradient vectors. Maximum and minimum values. §14.6,14.7 p.961-962: 1,2,3,5,6,7,8,15,27,28,29,30
Dec 4 Lagrange multipliers §14.8 p.970-971: 1,3,4,6,7,8,9,23,24 Problems set 10
Dec 6 Lagrange multipliers §14.8 Problems set 11
Dec 11 Review. Last day of class p.971: 18,19 Problems set 12
Dec 15 2pm. Dead line for extra credit
Dec 18 Final exam 1:10-4pm Practice final Solutions /td>