Introduction to Physical Mathematics

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences.

P.G. Harper (Author), D. L. Weaire (Author)

9780521269087, Cambridge University Press

Paperback, published 7 March 1985

276 pages
22.9 x 15.2 x 1.6 cm, 0.41 kg

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.

1. Introduction
2. Errors
3. Cartesian coordinates
4. Vectors
5. The scalar product
6. The vector product and rotation
7. Matrices in physics
8. The transformation of matrices
9. The matrix eigenvalue equation
10. Exponential and logarithm functions
11. Sine and cosine functions
12. Graph plotting and curve sketching
13. Differentiation
14. Approximations
15. Power series and Taylor's expansion
16. Partial differentiation
17. Integration
18. The differential equation
19. Solving first-order differential equations
20. Second-order differential equations
21. Solving second-order differential equations
22. The complex exponential
23. The circuit equation
24. Harmonics and Fourier series
25. The diffusion equation
26. Waves
27. The rate of change of a vector
28. The scalar field and gradient operator
29. The vector field
30. Line integration
31. The potential field
32. Surface and volume integration
33. Flux and divergence
34. Circulation and the curl
35. Conclusion
36. Miscellaneous exercises.

Subject Areas: Physics [PH]