Generalized Functions

Theory and Applications

Ram P. Kanwal

476 pages, parution le 27/10/2004 (3^eme édition)

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Résumé

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 physics….[it presents] a wealth of applications that cannot be found in any other single source…Kanwal 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 properties…. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology." Zentralblatt

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Ram P. Kanwal
Parution	27/10/2004
Édition	3^eme édition
Nb. de pages	476
Format	17,5 x 25,5
Couverture	Broché
Poids	864g
Intérieur	Noir et Blanc
EAN13	9780817643430
ISBN13	978-0-8176-4343-0