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

• Main Authors: Saichev, Alexander I. (Author, http://id.loc.gov/vocabulary/relators/aut), Woyczynski, Wojbor (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Applied and Numerical Harmonic Analysis,
• Subjects: Mathematical models.; Applied mathematics.; Engineering mathematics.; Fourier analysis.; Physics.; Mathematical Modeling and Industrial Mathematics.; Applications of Mathematics.; Fourier Analysis.; Mathematical Methods in Physics.; Engineering Mathematics.

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 rese...

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.