## Methods of Theoretical Physics I

Part I consists of eight chapters. It has 997 pages (plus a 14 page table of contents and a 40 page index). The table of contents, which is very detailed, has the following main headings.

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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