This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

- Cover
- Title Page
- Copyright
- Contents
- Preface
- Chapter 1. The Real Variable
- Chapter 2. Scalars and Vectors
- Chapter 3. Tensors
- Chapter 4. Matrices
- Chapter 5. Multiple Integrals
- Chapter 6. Potential Theory
- Chapter 7. Operational Methods
- Chapter 8. Physical Applications of the Operational Method
- Chapter 9. Numerical Methods
- Chapter 10. Calculus of Variations
- Chapter 11. Functions of a Complex Variable
- Chapter 12. Contour Integration and Bromwich’s Integral
- Chapter 13. Conformal Representation
- Chapter 14. Fourier’s Theorem
- Chapter 15. The Factorial and Related Functions
- Chapter 16. Solution of Linear Differential Equations of the Second Order
- Chapter 17. Asymptotic Expansions
- Chapter 18. The Equations of Potential, Waves, and Heat Conduction
- Chapter 19. Waves in One Dimension and Waves with Spherical Symmetry
- Chapter 20. Conduction of Heat in One and Three Dimensions
- Chapter 21. Bessel Functions
- Chapter 22. Applications of Bessel Functions
- Chapter 23. The Confluent Hypergeometric Function
- Chapter 24. Legendre Functions and Associated Functions
- Chapter 25. Elliptic Functions
- Notes
- Appendix on Notation
- Index