Mathematical Methods for Physics and Engineering

A Comprehensive Guide


1. Preliminary calculus
2. Complex numbers and hyperbolic functions
3. Series and limits
4. Partial differentiation
5. Multiple integrals
6. Vector algebra
7. Matrices and vector spaces
8. Vector calculus
9. Line, surface and volume integrals
10. Fourier series
11. Integral transforms
12. First order ODEs
13. Higher order ODEs
14. Series solutions of ordinary differential equations
15. Eigenfunction methods for differential equations
16. PDEs: general and particular solutions
17. PDEs: separation of variables and other methods
18. Complex variables
19. Tensors
20. Calculus of variations
21. Integral equations
22. Group theory
23. Representation theory
24. Probability
25. Numerical methods
Appendix. Special functions
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Mike Hobson, MRAO, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, UK