Math 136: Complex Variables and Integral Transforms

Homework 10



Read Sections 6.2, 6.3, and 6.4 of Saff and Snider,
and the summary at the end of Chapter 6.


Do these problems from Saff and Snider:

  • Sec. 6.2, Trigonometric Integrals: 1, 8, 9. (Explain the steps you use.)
    Hint for Q8: The denominator is not monic!
    Hint for Q9: Binomial theorem.
    (Think about 10.)
    You need only turn in two of these three questions. If you prefer to attempt all three, we will count your best two.
  • Sec. 6.3, Improper Integrals of Certain Functions: 7, 8, 9, 10.
    Hint for Q7: When you start computing the residues, let Q(z) = (z-z_2)(z-z_3)(z-z_4), and only plug in the specific values of Q(z_1), Q'(z_1), etc near the end.
    (Think about 15b.)
    You need only turn in three of these four questions. If you prefer to attempt all four, we will count your best three.
These questions require some stamina.
If you've never used scrap paper + clean copy for your homework, now's the time to start.

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