Principles and Techniques of Applied Mathematics
MATH 373

Homework Assignment #5

Due Monday, March 19, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the Brown and Churchill 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. Since many of the problems have the answers included, your work is what's important!

A nonempty subset of the assignment 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 you worked with on the assignment.

Chapter 3, pp. 63 - 64
Problems:   1, 3, 4

Note: For problem #4, an alternative to the suggestion is to simply use the 1-d heat equation itself, with proper units for u_t and u_xx.

Chapter 3, pp. 71 - 73
Problems:   2, 3, 4, 8

Note: For problems #2 and #3, be careful of the sign of the directional derivative at each endpoint. In both problems, K is the thermal conductivity of the material arising as the positive proportionality constant given by Fourier's law.

Chapter 3, pp. 86 - 87
Problems:   1

Additional Problem:
Show that the function u = -k/r with k an arbitrary constant and r = (x^2 + y^2 + z^2)^(1/2) is a harmonic function on R^3 - {0}.