Math 136: Complex Variables and Integral Transforms
Homework 5
Read Sections 4.2, 4.3, and 4.4 of Saff and Snider,
and the summary at the end of Chapter 4.
Do these problems from Saff and Snider:
- Sec. 4.2, Contour Integrals: (Draw the contour
of integration in each case.) 3d, 5, 6a,
11b, c, 14a.
(Think about 8, 10, 15 - precursor of the ML Lemma, 16, 17.)
- Sec. 4.3, Independence of Path: 1f, 2, 6,
7, 10. (Hint for Q 10: delta-epsilon definition of
continuity.)
(Think about 3, 4, 5.)
- Sec. 4.4, Cauchy's Integral Theorem: 10a,
14, 16, 17.
(Think about 6, 7, 10b-e, 11.)
Questions 6 and 7 in Section 4.4 are about the relationship between
analytic functions and conservative/irrotational vector
fields.
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