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

Description

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 textbook available to a wider audience. Front Matter ....Pages i-xx Front Matter ....Pages 1-1 Basic Definitions and Operations (Alexander I. Saichev, Wojbor Woyczynski)....Pages 3-35 Basic Applications: Rigorous and Pragmatic (Alexander I. Saichev, Wojbor Woyczynski)....Pages 37-72 Front Matter ....Pages 73-73 Fourier Transform (Alexander I. Saichev, Wojbor Woyczynski)....Pages 75-91 Asymptotics of Fourier Transforms (Alexander I. Saichev, Wojbor Woyczynski)....Pages 93-135 Stationary Phase and Related Methods (Alexander I. Saichev, Wojbor Woyczynski)....Pages 137-148 Singular Integrals and Fractal Calculus (Alexander I. Saichev, Wojbor Woyczynski)....Pages 149-182 Uncertainty Principle and Wavelet Transforms (Alexander I. Saichev, Wojbor Woyczynski)....Pages 183-244 Summation of Divergent Series and Integrals (Alexander I. Saichev, Wojbor Woyczynski)....Pages 245-285 Back Matter ....Pages 287-336