Fourier and Laplace Transforms
Fourier and Laplace Transforms

Author:

Publisher: Cambridge University Press

Published: 2003-08-07

Total Pages: 468

ISBN-13: 9780521534413

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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.

An Introduction to Laplace Transforms and Fourier Series
An Introduction to Laplace Transforms and Fourier Series

Author: P.P.G. Dyke

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 257

ISBN-13: 1447105052

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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.

Fourier Series and Integral Transforms
Fourier Series and Integral Transforms

Author: Allan Pinkus

Publisher: Cambridge University Press

Published: 1997-07-10

Total Pages: 204

ISBN-13: 9780521597715

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Textbook covering the basics of Fourier series, Fourier transforms and Laplace transforms.

Essentials of Mathematical Methods in Science and Engineering
Essentials of Mathematical Methods in Science and Engineering

Author: Selcuk S. Bayin

Publisher: John Wiley & Sons

Published: 2019-12-04

Total Pages: 1105

ISBN-13: 1119580285

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A comprehensive introduction to the multidisciplinary applications of mathematical methods, revised and updated The second edition of Essentials of Mathematical Methods in Science and Engineering offers an introduction to the key mathematical concepts of advanced calculus, differential equations, complex analysis, and introductory mathematical physics for students in engineering and physics research. The book’s approachable style is designed in a modular format with each chapter covering a subject thoroughly and thus can be read independently. This updated second edition includes two new and extensive chapters that cover practical linear algebra and applications of linear algebra as well as a computer file that includes Matlab codes. To enhance understanding of the material presented, the text contains a collection of exercises at the end of each chapter. The author offers a coherent treatment of the topics with a style that makes the essential mathematical skills easily accessible to a multidisciplinary audience. This important text: • Includes derivations with sufficient detail so that the reader can follow them without searching for results in other parts of the book • Puts the emphasis on the analytic techniques • Contains two new chapters that explore linear algebra and its applications • Includes Matlab codes that the readers can use to practice with the methods introduced in the book Written for students in science and engineering, this new edition of Essentials of Mathematical Methods in Science and Engineering maintains all the successful features of the first edition and includes new information.

Distribution Theory
Distribution Theory

Author: Gerrit Dijk

Publisher: Walter de Gruyter

Published: 2013-03-22

Total Pages: 120

ISBN-13: 3110298511

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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.

Fourier Transforms
Fourier Transforms

Author: Ian Naismith Sneddon

Publisher: Courier Corporation

Published: 1995-01-01

Total Pages: 564

ISBN-13: 9780486685229

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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.

Signals & System Analysis
Signals & System Analysis

Author: Dr. J. S. Chitode

Publisher: Technical Publications

Published: 2020-11-01

Total Pages: 578

ISBN-13: 9333223584

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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.

Complex Variables and the Laplace Transform for Engineers
Complex Variables and the Laplace Transform for Engineers

Author: Wilbur R. LePage

Publisher: Courier Corporation

Published: 2012-04-26

Total Pages: 516

ISBN-13: 0486136442

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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.

An Introduction to Fourier Analysis
An Introduction to Fourier Analysis

Author: Russell L. Herman

Publisher: CRC Press

Published: 2016-09-19

Total Pages: 402

ISBN-13: 1498773710

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This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.