Partial Differential Equations

Independent Study 12F

Instructor: Robert Jantzen
Student: Philip Burnham
CRN: 22255
Credits: 3

An elementary introduction to partial differential equations, using Maple to bring the subject to life. Materials will include several texts, handwritten course notes, computer algebra assistance in some calculations, and regular meetings (several times a week) for discussion of assigned readings. Problem sets will be assigned throughout the semester to make readings concrete through calculation.

Guiding Textbook: Advanced Engineering Mathematics by Robert Lopez, Unit 5: Boundary Value Problems for PDEs
[Amazon web page] [Maplesoft webpage] [Instructor manual]

UNIT V. Boundary Value Problems for PDEs
Chapter 24 Wave Equation
Chapter 25 Heat Equation
Chapter 26 Laplace's Equation on a Rectangle
Chapter 27 Nonhomogeneous Boundary Value Problems
Chapter 28 Time-Dependent Problems in Two Spatial Dimensions
Chapter 29 Separation of Variables in Non-Cartesian Coordinates
Chapter 30 Transform Techniques

Hard cover textbook (edition 2001) and Maple electronic version available from bob, who also has the complete Instructor Manual of worked solutions. We'll try to tackle something interesting with outside texts or web sources as well. Some physics applications like the Schroedinger equation for the hydrogen atom will be covered.

A terminal project and presentation will be determined as the course develops.

Some links:

Example. First HW problem from Chapter 24.1: A1. We approximate the exact Fourier series by its first 10 terms and animate the motion of the vibrating string showing its initial plucked state and its evolution, exaggerated in the vertical direction (look at axis tickmark labels):