Author | Kanwal, Ram P. author |
---|---|

Title | Generalized Functions [electronic resource] : Theory and Applications / by Ram P. Kanwal |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |

Edition | Third Edition |

Connect to | http://dx.doi.org/10.1007/978-0-8176-8174-6 |

Descript | XX, 476 p. 1 illus. online resource |

SUMMARY

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

CONTENT

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