Contents: 1. Warming up: Functions of a real variable. 2. Gaussian integrals, Stirlings formula and 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. Multi-valued 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 and Further Reading. Index.

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