Orthogonal Series and Boundary Value Problems

Evans M. Harrell, II, and James V. Herod

Copyright 1994,1995, 1996

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This is the short version of the index of the book. There is also a longer version with more description.

Contents for the Green Track

(Switch here to the Orthogonal Track)

PREFACE

INTRODUCTION

BACKGROUND MATERIAL

CHAPTER I: INTEGRAL EQUATIONS

Section 1.1 Geometry and integral operators
Section 1.2 The Fredholm Alternative Theorems
Section 1.3 Solving Y = KY + f where K has a separable kernel
Section 1.4 Solving Y = KY + f where K is small
Section 1.5 An alternate meaning for small
The Resolvent
Section 1.6 K does not have a separable kernel and is not small
A COMPENDIUM OF PROBLEMS

A test at this stage.

CHAPTER II: BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Section 2.1 More about function space
Section 2.2 Differential Operators and Their Adjoints
Section 2.3 The Fredholm Alternative Theorems
Section 2.4 A Method for Constructing Green's Function if the First Alternative holds
Section 2.4(cont) Two points, unmixed
Section 2.5 An Understanding of the Equation L(y) = d
Section 2.6 The Second Alternative
A COMPENDIUM OF PROBLEMS

A test at this stage.

CHAPTER III A TECHNIQUE FOR A STANDARD SECOND ORDER PDE

Section 3.1 Classification of Second Order Linear Equations
Section 3.2 Standard Forms for Second Order Linear Equations
Section 3.3 A Calculus Review (crude version)
Section 3.4 Green's Identities (crude version)
Section 3.5 Adjoints of Differential Operators (crude version)
Section 3.6 The Free Green Function and the Method of Images <