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.)

• Sec. 8.3, The Laplace Transform: 3d, 5c.
  (Think about 7, 8.)