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Distributions in the Physical and Engineering Sciences - Volume 1
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Distributions in the Physical and Engineering Sciences - Volume 1

Distributions in the Physical and Engineering Sciences - Volume 1

Distributional and Fractal Calculus, Integral Transforms and Wavelets

Alexander I. Saichev, Wojbor A. Woyczynski - Collection Applied and Numerical Harmonic Analysis

336 pages, parution le 31/12/1996

Résumé

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books 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 problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

Features

  • Application oriented exposition of distributional calculus, including solutions of ordinary differential equations. Abstract formalism is kept to a minimum.
  • Detailed coverage of asymptotic methods, including the stationary phase and steepest descent methods, for Fourier and other integral transforms from an applications perspective.
  • Modern topics such as fractional calculus, uncertainty principle, wavelets and multiresolution analysis.
  • Extensive use of real-word applications from fluid mechanics, wave propagation, optics, relaxation phenomena, etc., in examples and exercise sets. Selected solutions and answers to exercises are carefully worked-out at the end of the book.
  • Clear explanations, motivation, and illustration of all necessary mathematical concepts.

Sommaire

  • Introduction
  • Notation
  • Distributions and their Basic Applications
    • Basic Definitions and Operations
    • Basic Applications: Rigorous and Pragmatic
  • Integral Transforms And Divergent Series
    • Fourier Transform
    • Asymptotics of Fourier Transforms
    • Stationary Phase and Related Method
    • Singular Integrals and Fractal Calculus
    • Uncertainty Principle and Wavelet Transforms
    • Summation of Divergent Series and Integrals
  • A: Answers and Solutions
  • B: Bibliographical Notes
  • Index
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Alexander I. Saichev, Wojbor A. Woyczynski
Collection Applied and Numerical Harmonic Analysis
Parution 31/12/1996
Nb. de pages 336
Format 16 x 24
Couverture Relié
Poids 626g
Intérieur Noir et Blanc
EAN13 9780817639242
ISBN13 978-0-8176-3924-2

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