Fourier and Laplace Transforms PDF Download
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Author:
Publisher: Cambridge University Press
ISBN: 9780521534413
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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.
Author:
Publisher: Cambridge University Press
ISBN: 9780521534413
Category : Mathematics
Languages : en
Pages : 468
Get Book Here
Book Description
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.
Author: P.P.G. Dyke
Publisher: Springer Science & Business Media
ISBN: 1447105052
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Author: Allan Pinkus
Publisher: Cambridge University Press
ISBN: 9780521597715
Category : Mathematics
Languages : en
Pages : 204
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Book Description
Textbook covering the basics of Fourier series, Fourier transforms and Laplace transforms.
Author: J. K. Goyal
Publisher:
ISBN: 9788175567054
Category : Fourier transformations
Languages : en
Pages : 208
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Book Description
Author: Ian Naismith Sneddon
Publisher: Courier Corporation
ISBN: 9780486685229
Category : Mathematics
Languages : en
Pages : 564
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Book Description
Focusing on applications of Fourier transforms and related topics rather than theory, this accessible treatment is suitable for students and researchers interested in boundary value problems of physics and engineering. 1951 edition.
Author: Gerrit Dijk
Publisher: Walter de Gruyter
ISBN: 3110298511
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added. It is suitable for a one-semester course at the advanced undergraduate or beginning graduate level or for self-study.
Author: Dr. J. S. Chitode
Publisher: Technical Publications
ISBN: 9333223584
Category : Technology & Engineering
Languages : en
Pages : 578
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Book Description
The book is written for an undergraduate course on the Signals and Systems. It provides comprehensive explanation of continuous time signals and systems , analogous systems, Fourier transform, Laplace transform, state variable analysis and z-transform analysis of systems. The book starts with the various types of signals and operations on signals. It explains the classification of continuous time signals and systems. Then it includes the discussion of analogous systems. The book provides detailed discussion of Fourier transform representation, properties of Fourier transform and its applications to network analysis. The book also covers the Laplace transform, its properties and network analysis using Laplace transform with and without initial conditions. The book provides the detailed explanation of modern approach of system analysis called the state variable analysis. It includes various methods of state space representation of systems, finding the state transition matrix and solution of state equation. The discussion of network topology is also included in the book. The chapter on z-transform includes the properties of ROC, properties of z-transform, inverse z-transform, z-transform analysis of LTI systems and pulse transfer function. The state space representation of discrete systems is also incorporated in the book. The book uses plain, simple and lucid language to explain each topic. The book provides the logical method of explaining the various complicated topics and stepwise methods to make the understanding easy. The variety of solved examples is the feature of this book. The book explains the philosophy of the subject which makes the understanding of the concepts very clear and makes the subject more interesting.
Author: Wilbur R. LePage
Publisher: Courier Corporation
ISBN: 0486136442
Category : Technology & Engineering
Languages : en
Pages : 516
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Book Description
Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.
Author: G. B. Folland
Publisher: American Mathematical Soc.
ISBN: 0821847902
Category : Fourier analysis
Languages : en
Pages : 447
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Book Description
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.
Author: Wolfgang Arendt
Publisher: Springer Science & Business Media
ISBN: 3034850751
Category : Mathematics
Languages : en
Pages : 526
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Book Description
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
