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Index
DOVER BOOKS ON MATHEMATICS
Title Page
Copyright Page
Dedication
PREFACE
Table of Contents
CHAPTER 1 - LINEAR SPACES
1.1 FUNCTIONS
1.2 • VECTORS
1.3 • LINEAR SPACES
1.4 • FINITE-DIMENSIONAL LINEAR SPACES
1.5 • INFINITE-DIMENSIONAL LINEAR SPACES
CHAPTER 2 - ORTHOGONAL FUNCTIONS
2.1 • INNER PRODUCTS
2.2 • ORTHOGONAL FUNCTIONS AND VECTORS
2.3 • ORTHOGONAL SEQUENCES
2.4 • DIFFERENTIAL OPERATORS
2.5 • INTEGRAL OPERATORS
2.6 • CONVOLUTION AND THE DIRICHLET KERNEL
CHAPTER 3 - FOURIER SERIES
3.1 • MOTIVATION
3.2 • DEFINITIONS
3.3 • EXAMPLES OF TRIGONOMETRIC SERIES
3.4 • SINE AND COSINE SERIES
3.5 • THE GIBBS PHENOMENON
3.6 • LOCAL CONVERGENCE OF FOURIER SERIES
3.7 • UNIFORM CONVERGENCE
3.8 • CONVERGENCE OF FOURIER SERIES
3.9 • DIVERGENT SERIES
3.10 • GENERALIZED FUNCTIONS
3.11 • PRACTICAL REMARKS
CHAPTER 4 - LEGENDRE POLYNOMIALS AND BESSEL FUNCTIONS
4.1 • PARTIAL DIFFERENTIAL EQUATIONS
4.2 • THE INTUITIVE MEANING OF THE LAPLACIAN OPERATOR
4.3 • LEGENDRE POLYNOMIALS
4.4 • LAPLACE’S EQUATION IN SPHERICAL COORDINATES
4.5 • SPHERICAL HARMONICS
4.6 • BESSEL FUNCTIONS
CHAPTER 5 - HEAT AND TEMPERATURE
5.1 • THEORY OF HEAT CONDUCTION
5.2 • TEMPERATURE OF PLATES
5.3 • TEMPERATURE OF SOLIDS
5.4 • HARMONIC FUNCTIONS
5.5 • EXISTENCE THEOREMS
5.6 • HEAT FLOW
CHAPTER 6 - WAVES AND VIBRATIONS; HARMONIC ANALYSIS
6.1 • THE VIBRATING STRING
6.2 • THE ONE-DIMENSIONAL WAVE EQUATION
6.3 • THE WEIGHTED STRING
6.4 • STRING WITH VARIABLE TENSION AND DENSITY
6.5 • VIBRATING MEMBRANES
6.6 • WAVES IN TWO AND THREE DIMENSIONS
6.7 • THE FOURIER INTEGRAL
6.8 • ALGEBRAIC CONCEPTS IN ANALYSIS
SUPPLEMENTARY EXERCISES
APPENDIX: FUNCTIONS ON GROUPS
ANSWERS AND NOTES
INDEX
A CATALOG OF SELECTED - DOVER BOOKS
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