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Generalized Functions

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Synopses & Reviews

Publisher Comments:

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

Synopsis:

Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

Synopsis:

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

Table of Contents

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.

Product Details

ISBN:
9780817643430
Author:
Kanwal, Ram P.
Publisher:
Birkhauser
Location:
Boston, MA
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Probability & Statistics - General
Subject:
Generalized functions
Subject:
Theory of distributions (functional analysis)
Subject:
Functional Analysis
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
mathematical methods in physics
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
ordinary differential equations
Subject:
Integral equations
Subject:
Mathematics-Calculus
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Mathematical Physics
Subject:
Differential equations, partial
Subject:
Differential Equations
Copyright:
Edition Number:
3
Edition Description:
3rd ed. 2004
Publication Date:
20040723
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
496
Dimensions:
254 x 178 mm 860 gr

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Generalized Functions New Trade Paper
0 stars - 0 reviews
$126.25 In Stock
Product details 496 pages Springer - English 9780817643430 Reviews:
"Synopsis" by , Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
"Synopsis" by , 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
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