Mathematical Physics with Applications, Problems and Solutions

Contents: 1. Warming up: Functions of a real variable 2. Gaussian integrals, Stirlings formula, & some integrals 3. Some more functions 4. Generalized functions 5. Vectors and tensors 6. Vector calculus 7. A bit of fluid dynamics 8. Some more vector calculus 9. A bit of electromagnetism and special relativity 10. Linear vector spaces 11. A look at matrices 12. More about matrices 13. Infinite-dimensional vector spaces 14. Linear operators on a vector space 15. Operator algebras and identities 16. Orthogonal polynomials 17. Fourier series 18. Fourier integrals 19. Discrete probability distributions 20. Continuous probability distributions 21. Stochastic processes 22. Analytic functions of a complex variable 23. More on analytic functions 24. Linear response and analyticity 25. Analytic continuation and the gamma function 26. Multivalued functions and integral representations 27. Mobius transformations 28. Laplace transforms 29. Green function for the Laplacian operator 30. The diffusion equation 31. The wave equation 32. Integral equations, Bibliography & Further Reading, Index.