Homework due Friday, October 13

 Show that convolution is commutative:
f_{1} * f_{2} = f_{2} * f_{1}.
 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 Fouriertransforming the equation and initial condition).
 Express the solution in terms of the Green function H(xz).

 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 leftmoving and rightmoving 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