Mathematical Physics: Applications and Problems

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