Math 136: Complex Variables and Integral Transforms
## Homework 12
Read Sections 7.3 -- 7.6 of Saff and Snider, Do these problems from Saff and Snider: - Sec. 7.1, Invariance of Laplace's Equation: 3.
(Think about 1.) - Sec. 7.2, Geometric Considerations: 2, 10, 11c, e.
For Question 2, the book suggests mimicking a proof which can now be found on p.120 in section 3.3 (typo in book says 3.2). The following fact is useful for using Theorem 3 to prove continuity: A function f:D->C is continuous on D if and only if whenever E is an open set in C, its inverse image f^{-1}(E) is open in D. That is, iff `inverse images of open sets are open'. (Think about 7, 8, 9, and the rest of 11. The area formula in 9 uses the Jacobian from Section 2.4 Q15.) - Sec. 7.3, Moebius Transformations: 4, 11.
(Think about 1 (see Example 2), 6, 7c.)
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