03800nmm a2200409 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245009400158250001700252260004700269300004000316505079800356653002401154653002401178653002301202653002801225653002601253653002401279653003501303653003201338653002301370653001201393653003601405653002701441653003501468653001301503710003401516041001901550989003801569856007201607082001101679520170001690EB000615573EBX0100000000000000046865500000000000000.0cr|||||||||||||||||||||140122 ||| eng a97808176817461 aKanwal, Ram P.00aGeneralized FunctionshElektronische RessourcebTheory and Applicationscby Ram P. Kanwal a3rd ed. 2004 aBoston, MAbBirkhäuser Bostonc2004, 2004 aXX, 476 p. 1 illusbonline resource0 aPreface 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 aApplied mathematics aFunctional analysis aIntegral equations aEngineering mathematics aMathematical analysis aFunctional Analysis aPartial Differential Equations aApplications of Mathematics aIntegral Equations aPhysics aMathematical Methods in Physics aAnalysis (Mathematics) aPartial differential equations aAnalysis2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -2004 uhttps://doi.org/10.1007/978-0-8176-8174-6?nosfx=yxVerlag3Volltext0 a515.45 aThis 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