Math 136: Complex Variables and Integral Transforms

Homework 6



Read Sections 4.5 - 4.7 of Saff and Snider,
and the summary at the end of Chapter 4.

In Section 4.7, Applications to Harmonic Functions, pay particular attention to Poisson's Integral Formula, which is an explicit representation formula for harmonic functions, analogous to Cauchy's Integral Formula for analytic functions.


Do these problems from Saff and Snider:

  • Sec. 4.5, Cauchy's Integral Formula and its Consequences:
    3c, d, 5 [compute G'(i) only], 8, 14.
    (Think about 1, 2, 9, 10, 16.)
  • Sec. 4.6, Bounds for Analytic Functions: 5, 7, 10, 13, 14.
    (Think about 15, 18.)
  • Sec. 4.7, Applications to Harmonic Functions: 6, 8.
    (Think about 4, 7.)


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