Operational Calculus

International Series of Monographs in Pure and Applied Mathematics

By: Thomas K. Boehme

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eText | 1 August 2014 | Edition Number 2

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Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.

Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book.

This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.