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 1, pp. 17 - 18
Problems:   2, 3, 4

Note: For #4, the integral of e^u with u complex is done the same way as if u was real. For example, the integral of e^(ix) is (1/i)e^(ix). If you don't recall the definition of hyperbolic sine, sinh x, look it up in your Calculus textbook or try online at MathWorld (online mathematics encyclopedia).

Chapter 1, pp. 21 - 22
Problems:   1, 3, 6, 8

Additional Problems:

1. (a) Show that the product of an odd function and an even function results in an odd function.
   (b) Show that the product of two even functions is an even function.


2. (a) Show that the full Fourier series for an even function f(x) on -Pi < x < Pi is equivalent to the Fourier cosine series for f(x) on 0 < x < Pi.
   (b) Show that the full Fourier series for an odd function f(x) on -Pi < x < Pi is equivalent to the Fourier sine series for f(x) on 0 < x < Pi.