Homework due Friday, October 13

    1. Show that convolution is commutative: f1 * f2 = f2 * f1.
    2. Prove the convolution formula for the inverse Fourier transform of a product (notes, p. 52).
  1. Do the exercise on p. 59 of notes:
    1. Solve the heat equation by separation of variables (or, equivalently, by Fourier-transforming the equation and initial condition).
    2. Express the solution in terms of the Green function H(x-z).
    1. Haberman 10.4.10. [Solve it by Fourier's method, not d'Alembert's.]
    2. Show that your solution to 10.4.10 agrees with d'Alembert's solution by regrouping your formula into left-moving and right-moving terms.
  2. Haberman 10.5.16
  3. Haberman 10.6.13

Homework due Friday, October 20

  1. Do the exercise on p. 53 of notes ("Check that (*) is correct").
  2. Haberman 9.3.5. [Omit 9.3.5(b). Instead, insert 9.3.6(a) and use it to solve 9.3.5(c).]
  3. Haberman 10.4.3
  4. Haberman 10.6.10