Analytic Methods in Physics

Title
Preface
Contents
Chapter 1 Vector Analysis
1.1 Introduction
1.2 The Cartesian Coordinate System
1.3 Differentiation of Vector Functions
1.4 Integration of Vector Functions
1.5 Orthogonal Curvilinear Coordinates
1.6 Problems
1.7 Appendix I: Systbme International (SI) Units
1.8 Appendix 11: Properties of Determinants
1.9 Summary of Some Properties of Determinants
Chapter 2 Modern Algebraic Methods in Physics
2.1 Introduction
2.2 Matrix Analysis
2.3 Essentials of Vector Spaces
2.4 Essential Algebraic Structures
2.5 Problems
Chapter 3 Functions of a Complex Variable
3.1 Introduction
3.2 Complex Variables and Their Representations
3.3 The de Moivre Theorem
3.4 Analytic Functions of a Complex Variable
3.5 Contour Integrals
3.6 The Taylor Series and Zeros of f (z)
3.7 The Laurent Expansion
3.8 Problems
3.9 Appendix: Series
Chapter 4 Calculus of Residues
4.1 Isolated Singular Points
4.2 Evaluation of Residues
4.3 The Cauchy Residue Theorem
4.4 The Cauchy Principal Value
4.5 Evaluation of Definite Integrals
4.6 Dispersion Relations
4.7 Conformal Transformations
4.8 Multi-valued Functions
4.9 Problems
Chapter 5 Fourier Series
5.1 Introduction
5.2 The Fourier Cosine and Sine Series
5.3 Change of Interval
5.4 Complex Form of the Fourier Series
5.5 Generalized Fourier Series and the Dirac Delta Function
5.6 Summation of the Fourier Series
5.7 The Gibbs Phenomenon
5.8 Summary of Some Properties of Fourier Series
5.9 Problems
Chapter 6 Fourier Transforms
6.1 Introduction
6.2 Cosine and Sine Transforms
6.3 The Transforms of Derivatives
6.4 The Convolution Theorem
6.5 Parseval's Relation
6.6 Problems
Chapter 7 Ordinary Differential Equations
7.1 Introduction
7.2 First-Order Linear Differential Equations
7.3 The Bernoulli Differential Equation
7.4 Second-Order Linear Differential Equations
7.5 Some Numerical Methods
7.6 Problems
Chapter 8 Partial Differential Equations
8.1 Introduction
8.2 The Method of Separation of Variables
8.3 Green's Functions in Potential Theory
8.4 Some Numerical Methods
8.5 Problems
Chapter 9 Special Functions
9.1 Introduction
9.2 The Sturm-Liouville Theory
9.3 The Hermite Polynomials
9.4 The Helmholtz Differential Equation in Spherical Coordinates
9.5 The Helmholtz Differential Equation in Cylindrical Coordinates
9.6 The Hypergeometric Function
9.7 The Confluent Hypergeometric Function
9.8 Other Special Functions used in Physics
9.9 Problems
Chapter 10 Integral Equations
10.1 Introduction
10.2 Integral Equations with Separable Kernels
10.3 Integral Equations with Displacement Kernels
10.4 The Neurnann Series Method
10.5 The Abel Problem
10.6 Problems
Chapter 11 Applied Functional Analysis
11.1 Introduction
11.2 Stationary Values of Certain Functions and Functionals
11.3 Hamilton's Variational Principle in Mechanics
11.4 Formulation of Harniltonian Mechanics
11.5 Continuous Media and Fields
11.6 Transitions to Quantum Mechanics
11.7 Problems
Chapter 12 Geometrical Methods in Physics
12.1 Introduction
12.2 Transformation of Coordinates in Linear Spaces
12.3 Contravariant and Covariant Tensors
12.4 Tensor Algebra
12.5 The Line Element
12.6 Tensor Calculus
12.7 The Equation of the Geodesic Line
12.8 Special Equations Involving the Metric Tensor
12.9 Exterior Differential Forms
12.10 Problems
Bibliography
Index