Principles and Techniques of Applied Mathematics
MATH 373-01

Homework Assignment #4

Due Friday, March 4, 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 2.4, pp. 50 - 52
Problems:   11

Note: This problem proves some facts that we have repeatedly stated and used in class (we have even proved one case in class). There are two approaches for any case. One is straight-forward using substitution and change of variables (good practice.) The other is a bit more clever (this is the book's hint) and uses uniqueness. You may assume solutions to the wave equation (all time) and the diffusion equation (t > 0) are unique. Some extra credit will be given if you provide two proofs for each case.

Section 3.1, pp. 58 - 59
Problems:   1, 3

Section 3.2, pp. 64
Problems:   1, 5

Note: For these two problems on reflections of waves, you only need to solve for t > 0.