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Tables of Contents for Green's Functions and Boundary Value Problems
Chapter/Section Title
Page #
Page Count
Preface to the Second Edition
xi
2
Preface to the First Edition
xiii
 
0. Preliminaries
1
52
1. Heat Conduction
3
7
2. Diffusion
10
3
3. Reaction-Diffusion Problems
13
8
4. The Impulse-Momentum Law: The Motion of Rods and Strings
21
12
5. Alternative Formulations of Physical Problems
33
8
6. Notes on Convergence
41
5
7. The Lebesgue Integral
46
7
1. Green's Functions (Intuitive Ideas)
53
44
1. Introduction and General Comments
53
9
2. The Finite Rod
62
14
3. Maximum Principle
76
4
4. Examples of Green's Functions
80
17
2. The Theory of Distributions
97
104
1. Basic Ideas, Definitions, Examples
97
21
2. Convergence of Sequences and Series of Distributions
118
20
3. Fourier Series
138
20
4. Fourier Transforms and Integrals
158
21
5. Differential Equations in Distributions
179
22
3. One-Dimensional Boundary Value Problems
201
41
1. Review
201
6
2. Boundary Value Problems for Second-Order Equations
207
12
3. Boundary Value Problems for Equations of Order p
219
4
4. Alternative Theorems
223
11
5. Modified Green's Functions
234
8
4. Hilbert and Banach Spaces
242
75
1. Functions and Transformations
242
4
2. Linear Spaces
246
7
3. Metric Spaces, Normed Linear Spaces, Banach Spaces
253
12
4. Contractions
265
18
5. Hilbert Spaces
283
15
6. Separable Hilbert Spaces and Orthonormal Bases
298
14
7. Linear Functionals
312
5
5. Operator Theory
317
53
1. Basic Ideas and Examples
317
8
2. Closed Operators
325
4
3. Invertibility--The State of an Operator
329
6
4. Adjoint Operators
335
6
5. Solvability Conditions
341
5
6. The Spectrum of an Operator
346
11
7. Compact Operators
357
4
8. Extermal Properties of Operators
361
9
6. Integral Equations
370
65
1. Introduction
370
9
2. Fredholm Integral Equations
379
13
3. The Spectrum of a Self-Adjoint Compact Operator
392
9
4. The Inhomogeneous Equation
401
18
5. Variational Principles and Related Approximation Methods
419
16
7. Spectral Theory of Second-Order Differential Operators
435
56
1. Introduction; the Regular Problem
435
26
2. Weyl's Classification of Singular Problems
461
13
3. Spectral Problems with a Continuous Spectrum
474
17
8. Partial Differential Equations
491
106
1. Classification of Partial Differential Equations
491
14
2. Typical Well-Posed Problems for Hyperbolic and Parabolic Equations
505
20
3. Elliptic Equations
525
28
4. Variational Principles for Inhomogeneous Problems
553
44
9. Nonlinear Problems
597
86
1. Introductory Concepts
597
21
2. Branching Theory
618
8
3. Perturbation Theory for Linear Problems
626
12
4. Techniques for Nonlinear Problems
638
32
5. The Stability of the Steady State
670
13
Index
683