Math 136: Complex Variables and Integral Transforms

Homework 13

Read Sections 7.7, 8.2, and 8.3 of Saff and Snider,
and the summary at the end of Chapter 8.

Do these problems from Saff and Snider:

  • Sec. 7.5, The Schwarz-Christoffel Transformation: 2, 3.
    (Think about 8. We'd use a fifth vertex w_5 with turning angle zero (!), located at the midpoint of the top edge of the rectangle.)
  • Sec. 7.6, Electrostatics, Heat Flow, and Fluid Mechanics: 3, 11.
    Hint for Q3: Start by mapping to a half-disc.
    Hint for Q11: You may use the conformal mapping given in the Answers section for Q7, Section 7.5.
    You need only turn in three of the four questions assigned in Sections 7.5 + 7.6. If you prefer to attempt all four, we will count your best three.
  • Sec. 7.7, Further physical applications of conformal mapping: 7.
    (Think about 4, 6.)
  • Sec. 8.2, The Fourier Transform: 1b.
    Hint for Q1b: After you complete the square, I think you still have to do a contour integral.
    (Think about 7. This is the wave equation on the line, which we did in class.)

Recommended, but don't hand in:
  • Sec. 8.3, The Laplace Transform: 3d, 5c.
    (Think about 7, 8.)

The end!!

Return to Math 136 page