Homework due Friday, October 13

1. 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).
2. 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).
3. 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.
4. Haberman 10.5.16
5. 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