All problem numbers refer to the Strauss book,
the required text for the course. Unless otherwise indicated,
all parts of a problem (a), (b), etc. should be completed.
You should write up solutions neatly to all problems,
making sure to SHOW ALL YOUR WORK.
A nonempty subset will be graded. You are strongly encouraged to work
on these problems with other classmates, although the solutions you turn in
should be YOUR OWN WORK.
Important: Please list the names of any students or faculty who you worked with on the assignment.
Section 5.4, pp. 129 - 131
Problems: 2, 11
Note: Problem #2 should help solidify your understanding of the three types of convergence. You do not have to use epsilon-N notation in your proof unless you find it useful. Problem #11 was mentioned in class on Monday, April 25th. In part b), you are asked to find a formula for the coefficients of the full Fourier series of F(x) in terms of the Fourier coefficients for f(x).
Section 5.6, pp. 144 - 145
Problems: 1, 9
Hint: Both these problems should be solved using the method of subtraction.
The key is to figure out what to subtract. Try finding an easy solution U(x,t) (eg.
an equilibrium solution) that satisfies the PDE and the boundary conditions, then let
v(x,t) = u(x,t) - U(x,t) and solve to find v(x,t). Go the distance with these problems,
ie. find the series solution and the Fourier coefficients.