Mathematical Methods in Physics

Bol Partner

Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines. 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.Key Topics: Part I: A brief introduction to (Schwartz) distribution theory; Elements from the theories of ultra distributions and hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties of and basic properties for distributions are developed with applications to constant coefficient ODEs and PDEs; the relation between distributions and holomorphic functions is developed as well. * Part II: Fundamental facts about Hilbert spaces and their geometry. The theory of linear (bounded and unbounded) operators is developed, focusing on results needed for the theory of Schr"dinger operators. The spectral theory for self-adjoint operators is given in some detail. * Part III: Treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators, concludes with a discussion of the Hohenberg--Kohn variational principle. * Appendices: Proofs of more general and deeper results, including completions, metrizable Hausdorff locally convex topological vector spaces, Baire's theorem and its main consequences, bilinear functionals. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines. Physics has long been regarded as a wellspring of mathematical problems. ++Mathematical Methods in Physics++((kursiv)) 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. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines. A comprehensive bibliography and index round out the work.

Bol

This new book on Mathematical Methods In Physics is intended to be used for a 2-semester course for first year MA or PhD physics graduate students, or senior undergraduates majoring in physics, engineering or other technically related fields.Emphasis has been placed on physics applications, included where appropriate, to complement basic theories. Applications include moment of inertia in Tensor Analysis ; Maxwell's equations, magnetostatic, stress tensor, continuity equation and heat flow in fields ; special and spherical harmonics in Hilbert Space ; electrostatics, hydrodynamics and Gamma function in Complex Variable Theory ; vibrating string, vibrating membrane and harmonic oscillator in Ordinary Differential Equations ; age of the earth and temperature variation of the earth's surface in Heat Conduction ; and field due to a moving point charge (Lienard-Wiechart potentials) in Wave Equations .Subject not usually found in standard mathematical physics texts include Theory of Curves in Space in Vector Analysis , and Retarded and Advanced D-Functions in Wave Equations .Lastly, problem solving techniques are presented by way of appendices, comprising 75 pages of problems with their solutions. These problems provide applications as well as extensions to the theory.A useful compendium, with such excellent features, will surely make it a key reference text.