Math 136: Complex Variables and Integral Transforms

Homework 8



Read Sections 5.5-5.7 of Saff and Snider,
and the summary at the end of Chapter 5.

Section 5.4 has more rigorous proofs of the power series theorems.


Do these problems from Saff and Snider:

  • Sec. 5.3, Power Series: 3f, 4, 6, 8, 9, 13a, 15.
    (Think about 10, 11, 12, 16, 18.)
    You only need to turn in six of these seven questions. If you prefer to attempt all seven, we will count your best six.
  • Sec. 5.5, Laurent Series: 2, 5, 7a, 9, 10, 13.
    Hint for Q10: Eventually you get an integral expression for J_k(lambda). Look for some cancellation to show that the imaginary part is zero - the integrand is 'odd around pi'.
    You only need to turn in five of these six questions.
    If you prefer to attempt all six, we will count your best five.


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