# 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

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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.
## Chapter 1: Integral Equations

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Section 1 Geometry and a Linear Function

## Section 2 The Fredholm Alternative Theorems

## Section 4 The Kernel is Small

## Section 5 Alternate "K is Small"

## Section 6 Neither Small nor Separable

## Problems A Compendium of Problems

## Chapter 2: Ordinary Differential Equations

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Section 1 More About the Space

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Section 2 Differential Operators and Their Adjoints

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Section 3 The Fredholm Alternative Theorems

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Section 4 G(x,t) in the First Alternative

Section 5 G(x,t) and the Dirac Delta Distribution
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Section 6 G(x,t) in the Second Alternative

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Problems A Compendium of Problems

## Chapter 3: Partial Differential Equations

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Section 1 Classification for Second Order Equations

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Section 2 A Standard Form for Second Order Equations

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Section 4 Green's Identities

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Section 5 Adjoints of Differential Operators

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Section 6 Green's Functions for Dirichlet Problems in the Plane

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Section 7 A Maximum Principle

## Section 8 An Example: The Shape of a Drum