Homework due Friday, October 13
- Show that convolution is commutative:
f1 * f2 = f2 * f1.
- Prove the convolution formula for the inverse Fourier transform of a
product (notes, p. 52).
- Do the exercise on p. 59 of notes:
- Solve the heat equation by separation of variables (or, equivalently,
by Fourier-transforming the equation and initial condition).
- Express the solution in terms of the Green function H(x-z).
- Haberman 10.4.10. [Solve it by Fourier's method, not d'Alembert's.]
- 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.
- Haberman 10.5.16
- Haberman 10.6.13
- Do the exercise on p. 53 of notes ("Check that (*) is correct").
- Haberman 9.3.5. [Omit 9.3.5(b). Instead, insert 9.3.6(a) and use it
to solve 9.3.5(c).]
- Haberman 10.4.3
- Haberman 10.6.10