Principles and Techniques of Applied Mathematics
MATH 373

Homework Assignment #4

Due Friday, February 23, 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 2, pp. 39 - 40
Problems:   2, 5, 6, 8, 9

Chapter 2, pp. 42 - 45
Problems:   1, 3, 8

Note: In Problem #8, exp( ) is an abbreviation for the exponential function e^( ). The nice, single formula for Fourier coefficients derived here is often listed as the expression for Fourier series.

Chapter 2, pp. 54 - 56
Problems:   7

Note: Problem #7 illustrates the Gibbs phenomenon or overshoot ("ringing") of the Fourier series as it converges near a point of discontinuity. This problem may take a bit of work and persistence, but it demonstrates the power of mathematical analysis for explaining numerical (ie. computer) phenomenon.