Homework should be turned in at the BEGINNING OF CLASS.
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 4.3, pp. 97 - 100
Problems: 1, 2, 3, 4
Note: For problem #1, you are looking for solutions to X'' = -lambda X which satisfy the given boundary conditions (combination of Dirichlet and Robin.) Problem #3 refers to equations (16) and (17) in the text. Note that tanh(x) = sinh(x)/cosh(x). You should first show that the solution to the ODE (usually written in terms of exponentials) can be written in terms of cosh and sinh. For problem #4 there is an error in the hint: A negative sign should be multiplying the rational function on the second to last line.
Section 5.1, pp. 107 - 109
Problems: 2, 8, 9
Hint: For problem #9, use a trig identity involving cos^2(x).
Section 5.2, pp. 113 - 114
Problems: 2, 11, 15