Operational Calculus and Related Topics

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 Heavisides algebraic operational calculus and Paul Diracs delta function. Other discussions deal with the conditions for the existence of integral transforms, Jan Mikusiskis 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 Diracs 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.