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Introduction To The Operational Calculus

Calculus, Operational. --- Operational calculus --- Differential equations --- Electric circuits --- Integral equations

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Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics)

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This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Fourier transformations. --- Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- Transformations, Fourier --- Transforms, Fourier --- Fourier analysis

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Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and financial planners.

Calculus, Operational. --- Laplace transformation. --- Operational calculus --- Differential equations --- Electric circuits --- Integral equations --- Transformation, Laplace --- Calculus, Operational --- Transformations (Mathematics) --- Integral Transforms. --- Engineering mathematics. --- Integral Transforms, Operational Calculus. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Transform calculus --- Mathematics --- Integral transforms. --- Operational calculus. --- Applied mathematics.

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This volume contains six peer-refereed articles written on the occasion of the workshop "Operator theory, system theory and scattering theory: multidimensional generalizations and related topics", held at the Ben-Gurion University of the Negev from June 26 to July 1, 2005. The contributions which both survey their respective fields and contain new results present a cross-section of current activity in operator theory and system theory. Topics considered include Schur analysis, hierarchical semiseparable matrices, canonical forms for pairs of quaternionic matrices, the theory of homogeneous operators, algebras of fractions of continuous functions, and moment problems. Schur analysis in its various aspects occupies more than half of the volume, and moments problems have also an important place in the papers presented here. The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists. .

Operator theory --- Schur functions --- Moment problems (Mathematics) --- Quaternions --- Algebra, Universal --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex --- Vector analysis --- Calculus, Operational --- S-functions --- Schur's functions --- Holomorphic functions --- Operator theory. --- Global analysis (Mathematics). --- Operator Theory. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional analysis --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis