Principles and Techniques of Applied Mathematics
MATH 373-01

Homework Assignment #6

Due Friday, April 8, START of Class

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