Teaching Assistant: Irena Penev
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.
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.
(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.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 |