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.
General
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