Class Notes for Math 4348
Winter Quarter, 1998
Instructor: Professor Jim Herod
email:
herod@math.gatech.edu
Phone: (404) 894 9240 Fax: (404) 894 4409
Catalog Description: MATH 4348.
Solutions of boundary value problems for partial differential equations by Green's functions. Representative solutions for potential and diffusion equations. Applications.
Electronic Text
The text which follows is provided as an Adobe Acrobat file.
Each section is followed by a Maple construction to illustrate graphs and computations.
Introduction
Chapter 1: Integral Equations
Section 1 Geometry and a Linear Function
   Maple construction
for Section 1
Section 2 The Fredholm Alternative Theorems
   Maple construction
for Section 2
   Maple construction
for Section 3
Section 4 The Kernel is Small
   Maple construction
for Section 4
Section 5 Alternate "K is Small"
   Maple construction for Section 5
Section 6 Neither Small nor Separable
   Maple construction for Section 6
Problems A Compendium of Problems
Chapter 2: Ordinary Differential Equations
Section 1 More About the Space
   Maple construction
for Section 1
Section 2 Differential Operators and Their Adjoints
   Maple construction
for Section 2
Section 3 The Fredholm Alternative Theorems
   Maple construction
for Section 3
Section 4 G(x,t) in the First Alternative
Section 5 G(x,t) and the Dirac Delta Distribution
   Maple construction
for Section 5
Section 6 G(x,t) in the Second Alternative
   Maple construction
for Section 6
Problems A Compendium of Problems
Chapter 3: Partial Differential Equations
Section 1 Classification for Second Order Equations
   Maple construction
for Section 1
Section 2 A Standard Form for Second Order Equations
   Maple construction
for Section 2
Section 4 Green's Identities
Section 5 Adjoints of Differential Operators
Section 6 Green's Functions for Dirichlet Problems in the Plane
Section 7 A Maximum Principle
Section 8 An Example: The Shape of a Drum
   Maple construction
for the Appendix