Math 550 (Section 1)  University of South Carolina
D. Meade  Fall 1997

Homework Problems for Chapters 7 and 8 Integrals over Paths and Surfaces and The Integral Theorems of Vector Analysis

Section Page Problems
7.1  400 # 1^{∗}, 2ab, 3c^{∗}, 5, 7, 10a, 11^{∗}
7.2  417 # 1ab^{∗}c, 2, 4^{∗}, 9, 11^{∗}
7.3  427 # 2^{∗}, 3, 5^{∗}, 7, 12^{∗}
7.4  438 # 4^{∗}, 9, 13^{∗}, 14, 22b^{∗}c
7.5  446 # 2, 3, 5^{∗}, 7, 9, 10^{∗}
7.6  460 # 4, 6, 7^{∗}, 14, 15^{∗}
Review 462 # 1bc, 2a, 3a, 5^{∗}, 7, 8^{∗}, 9, 11, 17^{∗}, 18, 20, 21, 23^{∗}, 25, 26
8.1  476 # 1, 2, 4^{∗}, 7, 9^{∗}, 13, 15^{∗}, 20
8.2  490 # 2^{∗}, 5, 6^{∗}, 7, 11, 15^{∗}, 23^{∗}
8.3  501 # 3, 4^{∗}, 9^{∗}, 10, 14ab, 15a^{∗}
8.4  515 # 3^{∗}, 4b, 5c, 9^{∗}, 12, 13, 15, 18^{∗}
Review 552 # 1, 3^{∗}, 4, 7, 8^{∗}, 11, 13^{∗}, 15, 18, 20

\underline{Notes}

• Problems marked with an asterisk (^{∗}) will be collected and graded.

• These problems have been selected as the minimum amount of work that you should be doing for this course. Some problems will be straightforward computations; some will require the construction of a logical argument using the terminology and concepts discussed in class; some problems will require you to expand your knowledge (with given information) and apply this to a new setting.

• If you need more practice, there are many other problems in the text that are similar to the ones I have assigned.

• There is a section of review problems at the end of each chapter. None of these problems will be collected for grading. These problems should be a good test of your understanding of the main points in the chapter. I suggest solving these problems as one part of your preparation for an exam.

• Be sure you know how to do all of these problems. Do not hesitate to ask questions – in class, by e-mail, or during office hours.

• This is the final set of homework problems. As you can see, we still have a fair amount of material to cover. The topics in the last two chapters are applications of everything discussed in the course: tangent vectors, normal vectors, parameterizations, double integrals, triple integrals, ….

• The final exam will concentrate on the topics in Chapters 7 and 8. However, as mentioned above, you will need to be able to use many of the earlier methods and techniques to solve these problems.