# Integral Transforms in Science and Engineering

• Kurt Bernardo Wolf
Book

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

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

1. Front Matter
Pages 1-2
2. Kurt Bernardo Wolf
Pages 3-42
3. Kurt Bernardo Wolf
Pages 43-99
4. Kurt Bernardo Wolf
Pages 101-135
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

### 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