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Overview
Various related ideas are explored in this introductory survey, but no topic is treated thoroughly, since monographs are available on each topic separately. The Laplace transformation serves as a model for the developments of the operational properties of several other transformations. Further, it provides a connection to the Mikusinski calculus and generalized functions. The development of the Fourier transformation is followed by a different treatment of generalized functions (distributions). These introductions to generalized functions parallel the constructive approaches to the rational and real number systems. There are more examples than proofs, including applications in which the computations do not overwhelm the ideas. A calculus background and a scattering of other mathematical ideas is needed for self study. Deeper or lengthier problems are inserted along with simpler exercises. Several short tables of useful transform pairs are included.
Audience: Upper level undergraduates and beginning graduate students in mathematics, physics and engineering.
Synopsis
Various related ideas are explored in this introductory survey, but no topic is treated thoroughly, since monographs are available on each topic separately. The Laplace transformation serves as a model for the developments of the operational properties of several other transformations. Further, it provides a connection to the Mikusinski calculus and generalized functions. The development of the Fourier transformation is followed by a different treatment of generalized functions (distributions). These introductions to generalized functions parallel the constructive approaches to the rational and real number systems. There are more examples than proofs, including applications in which the computations do not overwhelm the ideas. A calculus background and a scattering of other mathematical ideas is needed for self study. Deeper or lengthier problems are inserted along with simpler exercises. Several short tables of useful transform pairs are included.
Audience: Upper level undergraduates and beginning graduate students in mathematics, physics and engineering.
Booknews
An introductory survey covering Laplace transformations, Mikusinski operators, Fourier transformations, generalized functions, and other transformations. Theorems are given without proofs. Contains tables of transforms, worked examples and exercises, problems of various lengths and levels of difficulty, and appendices on subjects including the Titchmarsh theorem and inversion integrals. For upper- level undergraduates and graduate students in mathematics, physics, and engineering, assuming a background in calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)