Week 9 (March 8 - March 12)

This week we start discussing partial differential equations. In particular, we will look at separation of variables and approximation of solutions using Fourier series. This semester, we will consider problems associated with the one-dimensional heat equation, the one-dimensional wave equation, and Laplace's equation in two space dimensions.

On Monday, we will make a quick survey of these equations and review the way Fourier approximations arise. On Wednesday, we will review what we know about Fourier series. On Friday, there will be an optional lab using the new module, Review of Fourier Series. I will use the grade from this report to replace any lower lab grade this semester. I will assign teams for this lab as students arrive on Friday. Only students who show up for the lab may submit a report. However, if you do not come to lab on Friday, I encourage you to work through this activity on your own.

Note: The module, Introduction to the One-Dimensional Heat Equation, provides a good review of the meaning and importance of boundary and initial conditions for a partial differential equation. Although this lab activity is not assigned, I encourage you to work through it. This module has no Maple worksheet; all the interaction is done with applets. Thus you can work on it from any machine with an internet connection and an up-to-date browser.

Homework due on Friday, March 12.

1. Introduction to Chapter 16: Problems 1- 6 on page 781. For Problem 1, also find a complex function f so that u is the real part of f. Beware: These problems are at the end of the Introduction, not at the end of Section 1.

2. Section 14.1: 1, 2, 3, 5, 6, 10

Last modified: March 12, 1999