Operational Calculus and Related Topics: 1st Edition (Hardback) book cover

Operational Calculus and Related Topics

1st Edition

By A. P. Prudnikov, K.A. Skórnik

Chapman and Hall/CRC

424 pages | 24 B/W Illus.

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pub: 2006-08-15
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Description

Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering. Operational Calculus and Related Topics highlights the classical methods and applications as well as the recent advances in the field.

Combining the best features of a textbook and a monograph, this volume presents an introduction to operational calculus, integral transforms, and generalized functions, the backbones of pure and applied mathematics. The text examines both the analytical and algebraic aspects of operational calculus and includes a comprehensive survey of classical results while stressing new developments in the field. Among the historical methods considered are Oliver Heaviside’s algebraic operational calculus and Paul Dirac’s delta function. Other discussions deal with the conditions for the existence of integral transforms, Jan Mikusiński’s theory of convolution quotients, operator functions, and the sequential approach to the theory of generalized functions.

Benefits…

· Discusses theory and applications of integral transforms

· Gives inversion, complex-inversion, and Dirac’s delta distribution formulas, among others

· Offers a short survey of actual results of finite integral transforms, in particular convolution theorems

Because Operational Calculus and Related Topics provides examples and illustrates the applications to various disciplines, it is an ideal reference for mathematicians, physicists, scientists, engineers, and students.

Reviews

“This book covers a reasonable portion of topics encountered in the theory and practice of operational calculi for functions of one real variable. It is intended and can be used both as an introductory text or a reference book for mathematicians, physicists and engineers. … chapters are packed with many examples of concrete computations of transforms of selected functions. …”

— In EMS Newsletter, June 2007

Table of Contents

INTEGRAL TRANSFORMS

Introduction to Operational Calculus

Integral Transforms — Introductory Remarks

The Fourier Transform

The Laplace Transform

The Mellin Transform

The Stieltjes Transform

The Hilbert Transform

Bessel Transforms

The Mehler–Fock Transform

Finite Integral Transforms

OPERATIONAL CALCULUS

Introduction

The Theorem of Titchmarsh

Operators

Bases of the Operator Analysis

Operators Reducible to Functions

Application of Operational Calculus

GENERALIZED FUNCTIONS

Introduction

Generalized  Functions — Functional Approach

Generalized Functions — Sequential Approach

Delta Sequences

Convergent Sequences

Local Properties

Irregular Operations

Hilbert Transform and Multiplication Forms

About the Series

Analytical Methods and Special Functions

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis