Generic Homework 4th Edition

Generic Outline and Homework Assignments

based on

VECTOR CALCULUS
Fourth Edition

Jerrold E. Marsden
Anthony Tromba

Version: December 22, 1996

PREAMBLE

Assuming 13 Weeks with 3 lecture hours per week and corresponding homework.
Adjust according to your own term length, level of the class, exams and holidays
Exercises below marked with ^ have a SOLUTION in the INSTRUCTORS GUIDE (this may be a help for TA's etc.) Keep in mind that Exercises with boxed numbers in the text have SOLUTION (sometimes only a partial solution) in the STUDENT GUIDE. These generally are not assigned as homework.
There is a mix of assigned problems; some for which answers are available to the student (odd numbers in the back of the book) and those for which answers are not available (all even numbered ones).

SYLLABUS AND HOMEWORK

Week 1: Review of Vectors, Matrices, Cylindrical and Spherical Coordinates.

Section 1.1, Page 22. #2, 5, 8, 16
Section 1.2, Page 36. #6, 19, 20, 24^
Section 1.3, Page 53. #4, 10^, 24^
Section 1.4, Page 63. #1, 4^, 12^
Section 1.5, Page 73. #1, 5, 12^

Note: If your class has not had any experience with 2 by 2 and 3 by 3 matrices, then you will need to spend 2 weeks or more on Chapter 1.

Week 2: Functions, Continuity and Differentiability

Section 2.1, Page 91. #2c, 15^, 29^
Section 2.2, Page 110. #6c, 8^, 10
Section 2.3, Page 122. #4d^, 8c^, 10^, 15, 18

Week 3: Paths, Properties of the Derivative, Gradients

Section 2.4, Page 132. #4, 11^, 18^
Section 2.5, Page 141. #2d, 3c, 8^, 12^,
Section 2.6, Page 152. #3c^, 5c, 6b, 16^
Section 2.R, Page 164. #13, 17, 20^, 22^, 42^

Note: Section 2.7 is more technical and exercises are not assigned. Of course if you are teaching an honors class or have selected good students, they should do exercises from this section.

Week 4: Iterated Partials, Taylor's Theorem, Extrema

Section 3.1, Page 179. #3a, 5, 9^, 12^
Section 3.2, Page 189. #2^, 3^, 6^
Section 3.3, Page 204. #1, 7^, 14^, 25^

Week 4: Lagrange Multipliers, Implicit Function Theorem, Applications

Section 3.4, Page 223. #2^, 7, 17, 20^
Section 3.5, Page 234. #3, 4^, 6^, 8^
Section 3.6, Page 241. #2^, 10^
Section 3.R, Page 242. #5^, 6, 24^

Note: Most people will want to assign something from section 3.5 on the implicit function theorem but vary the techncalities, as with section 2.7.

Note: The Instructors Guide Contains Practice Midterm Exam Questions at this Point

Week 5: Acceleration, Arc Length, Vector Fields

Section 4.1, Page 254. #3, 7^, 11^, 18^
Section 4.2, Page 262. #4^, 6, 18^
Section 4.3, Page 272. #3, 11^, 14^, 18^

Week 6: Divergence and Curl, Review

Section 4.4, Page 286. #3, 6, 10^, 15, 23, 26^
Section 4.R, Page 298. #4^, 11^, 16^, 27^, 28^

Week 7: Double Integrals

Section 5.1, Page 300. #1c^, 4^, 10^
Section 5.2, Page 313. #2c, 6^
Section 5.3, Page 321. #2a^, 6^, 13
Section 5.4, Page 326. #2a^, 4, 8^

Note: Exercises are not assigned from Section 5.5 on technical integration theorems. If you decide to lecture on this material of course you need to assign corresponding homework. In any case, the better students could be advised to read it and tor try some of the exercises.

Week 8: Triple Integrals and Review

Section 5.6, Page 346. #4^, 10, 11^
Section 5.R, Page 348. #3, 4^, 7, 11^, 13, 17

Week 9: Change of Variables and Applications

Section 6.1, Page 357. #3, 6^
Section 6.2, Page 372. #1, 6^, 8^, 9, 19^, 23^
Section 6.3, Page 384. #4^, 5^, 9, 14^, 15, 16
Section 6.4, Page 390. #1a, 4^, 6^
Section 6.R, Page 392. #4^, 12^, 17

Week 10: Line Integrals and Surfaces

Section 7.1, Page 400. #2^, 3a^, 6^
Section 7.2, Page 417. #2^, 6^, 15
Section 7.3, Page 297. #2^, 6^, 13^
Section 7.4, Page 460. #1, 6^, 15^

Week 11: Surface Integrals and Review

Section 7.5, Page 446. #1, 2^, 4^
Section 7.6, Page 460. #3^,7^, 15^
Section 7.R, Page 486. #3b^, 8, 11, 16^, 26^

Week 12: Green's and Stokes' Theorem

Section 8.1, Page 476. #3cd^, 6a, 13, 18
Section 8.2, Page 490. #3^, 6, 7, 8, 10^, 11, 14^, 23^, 25^.

Week 13: Conservative Fields, Gauss' Theorem, and Review

Section 8.3, Page 501. #4, 7, 10, 14^, 15^, 25^
Section 8.4, Page 515. #1, 2^, 5, 7^, 11^, 14^
Section 8.R, Page 552. #1, 3, 5, 10^, 11^, 15

Note: Exercises have not been assigned for Sections 8.5 and 8.6. As before, some of this should be assigned to the better students.

Note: At the end there are a lot of review problems and sample exams in both the Student Guide and the Instructors Guide. The students will love you if you hand out a sample exam. Let us know if you need the tex files for any of this.

POSTAMBLE

Note: If you have to shorten this syllabus due to time constraints, but sure to do so uniformly---it is critical that one treats Green's, Stokes' and Gauss' Theorems.

Good luck in your teaching of this material and please let us know if you have any suggestions for improvement!

Jerry Marsden: marsden@cds.caltech.edu
Tony Tromba: tromba@math.ucsc.edu