Distributions in the Physical and Engineering Sciences, Volume 1

1. Front Matter

   Pages i-xx

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2. Distributions and Their Basic Applications

   1. Front Matter

      Pages 1-1

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   2. Basic Definitions and Operations

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 3-35

   3. Basic Applications: Rigorous and Pragmatic

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 37-72

3. Integral Transforms and Divergent Series

   1. Front Matter

      Pages 73-73

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   2. Fourier Transform

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 75-91

   3. Asymptotics of Fourier Transforms

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 93-135

   4. Stationary Phase and Related Methods

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 137-148

   5. Singular Integrals and Fractal Calculus

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 149-182

   6. Uncertainty Principle and Wavelet Transforms

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 183-244

   7. Summation of Divergent Series and Integrals

      • Alexander I. Saichev, Wojbor Woyczynski

      Pages 245-285

4. Back Matter

   Pages 287-336

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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.

• Fourier transform
• Haar wavelet
• singular integral
• wavelets
• wavelet transform
• Cauchy integral

• Mathematical Department, State University of Nizhny Novgorod, Nizhny Novgorod, Russia

  Alexander I. Saichev

• Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, USA

  Wojbor Woyczynski

​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 Stochastic and Chaotic Processes in Science and Technology at Case Western University.

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