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AuthorKanwal, Ram P. author
TitleGeneralized Functions [electronic resource] : Theory and Applications / by Ram P. Kanwal
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004
Edition Third Edition
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Descript XX, 476 p. 1 illus. online resource


This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject. Key new topics and important features: * Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts * Enhanced presentation of the Schroedinger, Klein-Gordon, Helmholtz, heat and wave equations * Exposition driven by additional examples and exercises * Comprehensive bibliography and index * Prerequisites: advanced calculus, ordinary and partial differential equations ----- From the Reviewers: "Kanwal's book is a worthy member of this company [Gelfand and Shilov, Semanian, Friedman, Jones, and Barros-Neto]. Its strength lies in the application to classical physicsโ{128}ฆ.[it presents] a wealth of applications that cannot be found in any other single sourceโ{128}ฆKanwal has written a valuable book accessible to first-year graduate students in physics and engineering." --Ivar Stakgold, Mathematics, University of Delaware "The advantage of this text is in carefully gathered examples explaining how to use corresponding propertiesโ{128}ฆ. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology." --Zentralblatt


Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- The Dirac Delta Function and Delta Sequences -- The Schwartz-Sobolev Theory of Distributions -- Additional Properties of Distributions -- Distributions Defined by Divergent Integrals -- Distributional Derivatives of Functions with Jump Discontinuities -- Tempered Distributions and the Fourier Transforms -- Direct Products and Convolutions of Distributions -- The Laplace Transform -- Applications to Ordinary Differential Equations -- Applications to Partial Differential Equations -- Applications to Boundary Value Problems -- Applications to Wave Propagation -- Interplay between Generalized Functions and the Theory of Moments -- Linear Systems -- Miscellaneous Topics -- References -- Index

Mathematics Mathematical analysis Analysis (Mathematics) Functional analysis Integral equations Partial differential equations Applied mathematics Engineering mathematics Physics Mathematics Integral Equations Applications of Mathematics Analysis Functional Analysis Mathematical Methods in Physics Partial Differential Equations


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