Math V1201: Calculus III

Fall 2007

Instructor: Ciprian Manolescu

E-mail: cm@math.columbia.edu
Office: Mathematics 601
Office hours: Mondays 2:30 - 3:30 pm and Tuesdays 3-4 pm, or by appointment

Teaching Assistant: Irena Penev

E-mail: ipenev@math.columbia.edu
Office hours / Problem session: Mondays 7:30-8:30 pm, in Math 528.

Graders: Monica Nania (mn2225), Laura Peskin (lp2153).

Time and Place: 1:10 pm - 2:25 pm, Mondays and Wednesdays, 207 Mathematics Building

Web page: http://www.math.columbia.edu/~cm/calc3.html

Prerequisites: Calculus I (Math V1101), or equivalent.

Textbook: James R. Stewart, Calculus - Early Transcendentals, Sixth edition, Thomson Brooks/Cole. It is available at the university bookstore, and it is also on reserve in the Mathematics Library.

Material Covered: The "differentiable" part of multivariable calculus. Chapter 12, Vectors and the geometry of space; Sections 10.3 and 10.4, Polar coordinates; Section 10.5, Conics; Chapter 13, Vector functions; Chapter 14, Partial derivatives; Appendix G, Complex numbers; Sections 17.1 and 17.2, Ordinary Differential Equations.

Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final.

Homework: Homework will be assigned every week and will be due the following Wednesday, in class, by 2:25pm. The homework assignments will be posted on the web page. You must hand in the homework in class each Wednesday. You are encouraged to talk about the problems with other students, but you should write up the solutions individually. You should acknowledge the assistance of any book, student or professor. No late homework will be accepted! (The only exceptions are documented medical or family emergencies.) The lowest homework grade will be dropped.
Exams: There will be two midterms given in class, on Oct. 3 and Nov. 14. The final exam is projected by the University to be on Monday, December 17, between 1:10pm and 4:00pm. No make-up exams will be given.

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

Help: Help is available if you have trouble with the homework or the lecture material. If you are unable to come to my office hours, go to the Barnard Mathematics Help Room (Milbank 333). This room is always staffed by at least one mathematics professor or graduate student Monday through Thursday 10am-10pm, and on Friday 1pm-5pm. You may drop by whenever the Help Room is open; no appointment is necessary.

Weekly Schedule

(Check back for updates and changes!)

The listed exercises from the textbook are strongly recommended as practice, but they will not be collected. Answers for these are in the back of the book.

Problem sets are collected in class and returned in the mailboxes in front of the Undergraduate Office (Math 410).

Class	Topic	Read	Exercises	Due
Sep. 5	Coordinates and vectors	§12.1, 12.2	§12.1: 3, 5, 11, 15; §12.2: 7, 13, 17, 21
Sep. 7	Dot product	§12.3	§12.3: 1, 5, 7, 9, 17, 35
Sep. 12	Determinants and cross product	§12.4	§12.4: 1, 3, 13, 17, 19, 45	Homework 1: §12.1: 14, 34, 38; §12.2: 20, 24. Solutions
Sep. 17	Lines and planes	§12.5	§12.5: 3, 7, 17, 25, 33, 69, 71
Sep. 19	Intersections of lines and planes, Cramer's rule	Cramer's rule handout	§12.5: 19, 21, 43, 51, 57	Homework 2: §12.3: 28, 52; §12.4: 18, 38. Solutions
Sep. 24	Conics and quadrics	§10.5, 12.6	§10.5: 7, 13, 23, 55; §12.6: 21-28, 43
Sep. 26	Polar coordinates	§10.3, 10.4	§10.3: 17, 29, 35; §10.4: 1, 13, 29, 45	Homework 3: §12.5: 34, 38, 62, 74, 76. Solutions
Oct. 1	Review	Ch. 12 and §10.3-10.5	Preparation for Midterm I
Oct. 3	Midterm I. Statistics	Solutions:Version A, Version B

Class	Topic	Read	Due
Oct. 8	Vector functions and space curves	§13.1, 13.2	Oct.9: Last day to drop a class
Oct. 10	Arc length and curvature	§13.3	Homework 4: §13.1: 4, 12, 16, 38; §13.2: 4, 32, 34, 40. Solutions
Oct. 15	Motion in space: velocity and acceleration	§13.4
Oct. 17	Functions of several variables	§14.1	Homework 5: §13.3: 2, 12, 14, 18, 22, 36, 44, 46. Extra credit: 53, 54, 55. Solutions
Oct. 22	Limits and continuity	§14.2
Oct. 24	Partial derivatives	§14.3	Homework 6: §13.4: 6, 12, 16, 34; §14.1: 10, 20, 22, 24, 30, 46, 56. Extra credit: §13.4: 40; Problem 6 on p. 853. Solutions
Oct. 29	Tangent planes and linear approximations	§14.4
Oct. 31	Chain rule in several variables	§14.5	Homework 7: §14.2: 6, 12, 14, 20, 40; §14.3: 16, 18, 32, 48, 62. Extra credit: §14.2: 44; §14.3: 94. Solutions
Nov. 5	University holiday
Nov. 7	Directional derivatives and gradient vectors	§14.6	Homework 8: §14.4: 6, 21, 30, 32; §14.5: 2, 10, 22, 28, 32, 46. Extra credit: §14.4: 46 (You can assume the result of Exercise 45.) Solutions
Nov. 12	Review	Ch. 13 and §14.1-14.6
Nov. 14	Midterm II. Solutions. Statistics	§12.3	No homework this week. Preparation for Midterm II with Solutions to practice problems. Try also a Practice exam from last year (Prof. Thurston), with Answers
Nov. 19	Critical points of two-variable functions	§14.7
Nov. 21	Lagrange multipliers	§14.8	No homework
Nov. 26	Arithmetic of complex numbers	Appendix G, Complex numbers handout
Nov. 28	The complex exponential	Appendix G, Complex numbers handout	Homework 9: §14.7: 8, 12 (no graphing necessary), 30, 34, 42, 48, 50; §14.8: 4, 6, 8, 16, 42(b). Extra credit: Problem 8 on p. 949. Solutions
Dec. 3	Differential equations	§17.1
Dec. 5	Nonhomogeneous differential equations	§17.2; ignore the method of variation of parameters	Homework 10: Exercises 1-9 on the Complex numbers handout. Solutions
Dec. 10	Review	Everything
Dec. 17	Final. Solutions. Statistics	Preparation for the Final Exam with Solutions to the ODE practice problems and Solutions to other practice problems. Try also a Practice exam from last year (Prof. Thurston), with Answers

In preparation for the final, I will have office hours on Friday Dec. 14, 3-5 pm (in Math 601) instead of Tuesday. Also, Irena Penev will have a review session on Thursday Dec. 13, from 2-3pm, in Math 528.