Operational Calculus and Related Topics

Operational Calculus and Related Topics

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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 Mikusinski'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.show more

Product details

  • Hardback | 424 pages
  • 180.3 x 254 x 27.9mm | 907.2g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 24 black & white illustrations
  • 1584886498
  • 9781584886495

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 Formsshow more