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Distribution Theory And Transform Analysis


Author : A.H. Zemanian
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30



Download Distribution Theory And Transform Analysis written by A.H. Zemanian and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.


Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

Generalized Functions And Partial Differential Equations


Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30



Download Generalized Functions And Partial Differential Equations written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.


This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.

An Introduction To Fourier Analysis And Generalised Functions


Author : M. J. Lighthill
language : en
Publisher: Cambridge University Press
Release Date : 1958



Download An Introduction To Fourier Analysis And Generalised Functions written by M. J. Lighthill and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Mathematics categories.


"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress

Introduction To Analysis


Author : Maxwell Rosenlicht
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04



Download Introduction To Analysis written by Maxwell Rosenlicht and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.


Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

An Introduction To Black Holes Information And The String Theory Revolution


Author : Leonard Susskind
language : en
Publisher: World Scientific
Release Date : 2005-01-01



Download An Introduction To Black Holes Information And The String Theory Revolution written by Leonard Susskind and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Science categories.


- A unique exposition of the foundations of the quantum theory of black holes including the impact of string theory, the idea of black hole complementarily and the holographic principle bull; Aims to educate the physicist or student of physics who is not an expert on string theory, on the revolution that has grown out of black hole physics and string theory

A Guide To Distribution Theory And Fourier Transforms


Author : Robert S. Strichartz
language : en
Publisher: World Scientific
Release Date : 2003



Download A Guide To Distribution Theory And Fourier Transforms written by Robert S. Strichartz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.

Signals And Systems


Author : Alan V. Oppenheim
language : en
Publisher:
Release Date : 2013-07-29



Download Signals And Systems written by Alan V. Oppenheim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-29 with Signal theory (Telecommunication) categories.


For undergraduate-level courses in Signals and Systems. This comprehensive exploration of signals and systems develops continuous-time and discrete-time concepts/methods in parallel -- highlighting the similarities and differences -- and features introductory treatments of the applications of these basic methods in such areas as filtering, communication, sampling, discrete-time processing of continuous-time signals, and feedback. Relatively self-contained, the text assumes no prior experience with system analysis, convolution, Fourier analysis, or Laplace and z-transforms.