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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 practioners and researchers. The goal of the book is to give the reader, specialist and non-specialist useable 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.
List 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.
