Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work.

Preface * Introduction * Spaces of test functions * Schwartz distributions * Calculus for distributions * Distributions as derivatives of functions * Tensor products * Convolution products * Applications of convolution * Holomorphic functions * Fourier Transformation * Distributions and analytic functions * Other spaces of generalized functions * Hilbert spaces: A brief historical introduction * Inner product spaces and Hilbert spaces * Geometry of Hilbert spaces * Separable Hilbert spaces * Direct sums and tensor products * Topological aspects * Linear operators * Quadratic forms * Bounded linear operators * Special classes of bounded operators * Self-adjoint Hamilton operators * Elements of spectral theory * Spectral theory of compact operators * The spectral theorem * Some applications of the spectral representation * Introduction * The direct methods in the calculus of variations * Differential calculus on Banach spaces and extrema of differentiable functions * Constrained minimization problems (Method of Lagrange multipliers) * Boundary and eigenvalue problems * Density functional theory of atoms and molecules * Appendices * References * Index