Chapter 1 Types of Fields

1.1 Scalar Fields

1.2 Vector Fields

1.3 Curvilinear Coordinates

1.4 The Differential Operator ∇

1.5 Vector and Tensor Formalism

1.6 Dyadics and Other Vector Operators

1.7 The Lorentz Transformation, Four Vectors, Spinors

Problems

Table of Useful and Dyadic Equations

Table of Properties of Curvilinear Coordinates

Bibliography

Chapter 2 Equations Governing Fields

2.1 The Flexible String

2.2 Waves in an Elastic Medium

2.3 Motion of Fluids

2.4 Diffusion and Other Perculative Fluid Motion

2.5 The Electromagnetic Field

2.6 Quantum Mechanics

Problems

Standard Forms for Some of the Partial Differential

             Equations of Theoretical Physics

Bibliography

 
Chapter 3 Fields and the Variational Principle

3.1 The Variational Integral and Euler Equations

3.2 Hamilton's Principle and Classical Dynamics

3.3 Scalar Fields

3.4 Vector Fields

Problems

Tabulation of Variational Method

Bibliography

Chapter 4 Functions of a Complex Variable

4.1 Complex Numbers and Variables

4.2 Analytic Functions

4.3 Derivatives of Analytic Functions, Taylor and Laurent Series

4.4 Multivalued Functions

4.5 Calculus of Residues; Gamma and Elliptic Functions

4.6 Asymptotic series: Method of Steepest Descent

4.7 Conformal Mapping

4.8 Fourier Integrals

Problems

Tabulation of Properties of Functions of Complex Variable

Tables of Special Functions of General Use

Bibliography

Chapter 5 Ordinary Differential Equations

5.1 Separable Coordinates

5.2 General Properties, Series Solutions

5.3 Integral Representations

Problems

Table of Separable Coordinates in Three Dimensons

Second Order Differential Equations and Their Solutions

Bibliography

 
Chapter 6 Boundary Conditions and Eigenfunctions

6.1 Types of Equations and of Boundary Conditions

6.2 Difference Equations and Boundary Conditions

6.3 Eigenfunctions and Their Use

Problems

Table of Useful Eigenfunctions and Their Properties

Eigenfunctions by the Factorization Method

Bibliography

Chapter 7 Green's Functions

7.1 Source Points and Boundary Points

7.2 Green's Functions for Steady Waves

7.3 Green's Function for the Scalar Wave Equation

7.4 Green's Function for Diffusion

7.5 Green's Function in Abstract Vector Form

Problems

Table of Green's Functions

Bibliography

Chapter 8 Integral Equations

8.1 Integral Equations of Physics, Their Classification

8.2 General Properties of Integral Equations

8.3 Solution of Fredholm Equations of the First Kind

8.4 Solution of Integral Equations of the Second Kind

8.5 Fourier Transforms and Integral Equations

Table of Integral Equations and Their Solutions

Bibliography

Index