| A Biochem version of this document is available. |
(Jump down to Syllabus)
Subject matter: Differentiation and integration of functions of several variables, parametric curves and surfaces, optimization, vector fields, line and surface integrals, Stokes’ theorem and the divergence theorem.
Prerequisites: Math 1b with a satisfactory grade, or AB-BC score of at least 4, or scores of at least 20, 8, 4 on HMPT.
Course Head: Wilfried Schmid, Science Center 519, 495-7840; email: schmid@math; office hours on Tuesdays and Thursdays, 2:00 – 3:00.
Textbook: Thomas and Finney, Calculus and Analytic Geometry, Part II, 9th Edition.
Classes and problem sessions: This course is taught in sections, which meet three hours per week. In addition to the section meetings, you are expected to attend problem sessions, conducted weekly, by a Course Assistant. The Course Assistant also attends section meetings, grades the homework, and holds office hours. Occasionally, short quizzes will be given in the problem sessions; your performance on these quizzes will never count against you. You may attend more than one problem session per week – the schedule of all the sessions will be posted on this site and also on the Calculus Office bulletin board (outside Science Center 308).
Special sections: The various sections cover
the same material in the same order, with the following exceptions:
a) Two Biochemistry sections will emphasize applications
of multivariable calculus in the life sciences, and will also cover basic
probability theory;
b) Two Physics sections put greater weight on physical
motivation and applications of multivariable calculus;
c) A Mathematics section is designed to provide better
preparation for prospective mathematics concentrators.
Homework: Problems will be assigned during every section meeting, and will be due at the next meeting. You are encouraged to discuss the homework with your fellow students, but you must write up the solutions by yourself. Late homework will not be accepted. Your five lowest (four lowest in Tuesday-Thursday sections) homework scores will be disregarded when your average homework grade is computed.
Exams: Two course-wide midterms and a final. The midterms will take place on October 19 and December 1, in both cases from 7:30 until 9:30 pm; on October 19, in Science Center Halls C and D, and on December 1, in Halls A and C. The use of electronic calculators is not permitted during exams; in any case, calculators would be of little or no help.
Grading: Do not feel that you are competing for grades with your fellow students. If the course as a whole does better (or worse) than expected, we shall not hesitate to assign grades that are higher (or lower) on average than in previous years. Your final grades will be based on your performance on the homework (20%), the two midterms (20% each), and the final (40%). A small upward adjustment will be made in cases where the final is dramatically better than the average of the midterms and the homework.
Some words of caution: This course is fast
paced. “Taking it easy” in the beginning of the course and trying
to catch up later is an even riskier strategy than it would have been in
your earlier math courses. By the very nature of the material, memorizing
formulas and “plugging in values” is not enough. Numerical calculations
are still important, but play a smaller role than in one variable calculus.
While we shall not attempt to teach you proofs or rigorous arguments, we
do expect you to understand the important concepts. You will encounter
homework problems and exam problems that differ significantly from problems
you have seen in class.
Syllabus: Each
topic corresponds roughly to one hour of class time. The indicated
reading refers to sections in the textbook.
| 1. Vectors, dot products: 10.1, 10.2, 10.3 | 19. Multiple integrals, continued. |
| 2. Cross products, lines, planes: 10.4, 10.5 | 20. Double integrals in polar form: 9.6, 13.3 |
| 3. More lines and planes, distances from points
and planes: 10.5 |
21. Triple integrals in cylindrical and spherical
coordinates: 13.6, 13.7 |
| 4. Parametric curves: 11.1, 11.2 | 22. Vector fields, line integrals: 14.1, 14.2 |
| 5. Arc length, unit tangent vector: 11.3 | 23. More on vector fields and line integrals. |
| 6. Planetary motion: 11.5 | 24. Path independence: 14.3 |
| 7. Functions of several variables: 12.1 | 25. Green’s theorem: 14.4 |
| 8. Partial derivatives: 12.3 | 26. Surface area, flux: 14.5, 14.6 |
| 9. Differentiability, linearization: 12.4 | 27. Review |
| 10. Chain rule: 12.5, parts of 12.6 | 28. More on surface area and flux. |
| 11. Review | 29. Stokes’ theorem: 14.7 |
| 12. The gradient, tangent planes, directional derivatives: 12.7 | 30. More on Stokes’ theorem. |
| 13. More on the gradient. | 31. The divergence theorem: 14.8 |
| 14. Extrema, second derivative test: 12.8 | 32. More on the divergence theorem. |
| 15. Lagrange multipliers: 12.9 | 33. Tying things together. |
| 16. More on extrema. | 34. Review |
| 17. Multiple integrals, Fubini’s theorem: 13.1, parts of 13.4 | |
| 18. Examples of multiple integrals: 13.2, 13.5 |
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Last Updated: Oct 1, 1998 by Ralph
Teixeira