Distributions in the Physical and Engineering Sciences, Volume 1: Distributional and Fractal Calculus, Integral Transforms and Wavelets

by Alexander I. Saichev, Wojbor Woyczynski

Overview

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practitioners and researchers. The goal of the book is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. The present, softcover reprint is designed to make this classic textbookavailable to a wider audience.

Product Details

ISBN-13:	9783319979571
Publisher:	Springer International Publishing
Publication date:	08/29/2018
Series:	Applied and Numerical Harmonic Analysis
Edition description:	1st ed. 2018
Pages:	336
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Alexander I. Saichev was Professor of Mathematics at the Radio Physics Faculty of the Nizhny Novgorod University and a Professor in the Department of Management, Technology, and Economics at the Swiss Federal Institute of Technology.

Wojbor A. Woyczynski is Professor of Mathematics and Director of the Center for Shastic and Chaotic Processes in Science and Technology at Case Western University.

Table of Contents

I Distributions and their Basic Applications.- 1 Basic Definitions and Operations.- 2 Basic Applications: Rigorous and Pragmatic.- II Integral Transforms and Divergent Series.- 3 Fourier Transform.- 4 Asymptotics of Fourier Transforms.- 5 Stationary Phase and Related Method.- 6 Singular Integrals and Fractal Calculus.- 7 Uncertainty Principle and Wavelet Transforms.- 8 Summation of Divergent Series and Integrals.- A Answers and Solutions.- A.1 Chapter 1. Definitions and operations.- A.2 Chapter 2. Basic applications.- A.3 Chapter 3. Fourier transform.- A.4 Chapter 4. Asymptotics of Fourier transforms.- A.5 Chapter 5. Stationary phase and related methods.- A.6 Chapter 6. Singular integrals and fractal calculus.- A.7 Chapter 7. Uncertainty principle and wavelet transform.- A. 8 Chapter 8. Summation of divergent series and integrals.- B Bibliographical Notes.

Editorial Reviews

A textbook for a graduate or advanced undergraduate course covering miscellaneous mathematical tools useful to scientists and engineers, including equations of mathematical physics, special functions, and integral transforms. Assumes three to four semesters of calculus that covered elementary differential equations, Fourier series, complex variables, and linear algebra. Assumes no background in probability. Basic computer programming competence is also required. Annotation c. by Book News, Inc., Portland, Or.

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