Week 13 (April 12 - April 16)

This week and the next we will devote to the Laplace transform. On Monday of this week, we will introduce the Laplace transform and compare it to it's cousin, the Fourier transform. Then we will look at the use of the Laplace transform in solving initial value problems for ordinary differential equations. On Wednesday, we will examine those properties of the Laplace transform that will enable us to apply it to the solution of an initial value problem for the heat equation. Then on Friday, we will meet in the lab to investigate examples of both applications in the module, Experiments with the Laplace Transform.

Homework due on Friday, April 16 .

1. Section 3.1: 1, 3, 4, 8, 11, 13

2. Section 3.2: 1, 2, 4, 6

3. Section 3.4: 1-4, 9, 11, 13

4. Show that the differential equation
   d²U/dx² = s U - 1,

   where s is a positive parameter and x is the independent variable, has solutions of the form

   U = a(s) exp(sqrt(s)*x) + b(s) exp(-sqrt(s)*x) + 1/s.

   You will need this in the lab on Friday.

Last modified: April 14, 1999