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Integral Transforms in Science and Engineering

  • Kurt Bernardo Wolf

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 11)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Finite-Dimensional Vector Spaces and the Fourier Transform

  3. Fourier and Bessel Series

    1. Front Matter
      Pages 137-138
    2. Kurt Bernardo Wolf
      Pages 139-194
    3. Kurt Bernardo Wolf
      Pages 195-220
    4. Kurt Bernardo Wolf
      Pages 221-251
  4. Fourier and Related Integral Transforms

    1. Front Matter
      Pages 253-254
    2. Kurt Bernardo Wolf
      Pages 255-332
    3. Kurt Bernardo Wolf
      Pages 333-378
  5. Canonical Transforms

    1. Front Matter
      Pages 379-379
    2. Kurt Bernardo Wolf
      Pages 381-416
    3. Kurt Bernardo Wolf
      Pages 417-444
  6. Back Matter
    Pages 445-489

About this book

Introduction

Integral transforms are among the main mathematical methods for the solution of equations describing physical systems, because, quite generally, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one can often bring about a mathematical uncoupling of the equations in such a way that the solution becomes that of noninteracting constituents. The "tilt" in the reference frame is a finite or integral transform, according to whether the system has a finite or infinite number of elements. The types of coupling which yield to the integral transform method include diffusive and elastic interactions in "classical" systems as well as the more common quantum-mechanical potentials. The purpose of this volume is to present an orderly exposition of the theory and some of the applications of the finite and integral transforms associated with the names of Fourier, Bessel, Laplace, Hankel, Gauss, Bargmann, and several others in the same vein. The volume is divided into four parts dealing, respectively, with finite, series, integral, and canonical transforms. They are intended to serve as independent units. The reader is assumed to have greater mathematical sophistication in the later parts, though.

Keywords

Canon Finite Lattice Mathematica Volume equation form integral integral transform interaction system types

Authors and affiliations

  • Kurt Bernardo Wolf
    • 1
  1. 1.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMéxico D.F.México

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-0872-1
  • Copyright Information Springer Science+Business Media New York 1979
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0874-5
  • Online ISBN 978-1-4757-0872-1
  • Buy this book on publisher's site