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Mathematical Methods in Physics - Distributions, Hilbert Space Operators, and Variational Methods (Hardcover, 2003 ed.)
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Mathematical Methods in Physics - Distributions, Hilbert Space Operators, and Variational Methods (Hardcover, 2003 ed.)
Series: Progress in Mathematical Physics, 26
Expected to ship within 10 - 15 working days
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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 Schroedinger 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 broadcommunity of graduate
students in mathematics, mathematical physics, physics and
engineering, as well as researchers in these disciplines. Requisite
knowledge for the reader includes differential and integral
calculus, linear algebra, and some topology. Some basic knowledge
of ordinary and partial differential equations will enhance the
appreciation of the presented material.
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