Fourier and Laplace Transforms

Fourier and Laplace Transforms
Author:
Publisher: Cambridge University Press
Total Pages: 468
Release: 2003-08-07
Genre: Mathematics
ISBN: 9780521534413

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
Total Pages: 257
Release: 2012-12-06
Genre: Mathematics
ISBN: 1447105052

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
Total Pages: 204
Release: 1997-07-10
Genre: Mathematics
ISBN: 9780521597715

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

Distribution Theory

Distribution Theory
Author: Gerrit Dijk
Publisher: Walter de Gruyter
Total Pages: 120
Release: 2013-03-22
Genre: Mathematics
ISBN: 3110298511

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.

Essentials of Mathematical Methods in Science and Engineering

Essentials of Mathematical Methods in Science and Engineering
Author: Selcuk S. Bayin
Publisher: John Wiley & Sons
Total Pages: 1105
Release: 2019-12-04
Genre: Mathematics
ISBN: 1119580285

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.

Fourier Transforms

Fourier Transforms
Author: Ian Naismith Sneddon
Publisher: Courier Corporation
Total Pages: 564
Release: 1995-01-01
Genre: Mathematics
ISBN: 9780486685229

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
Total Pages: 578
Release: 2020-11-01
Genre: Technology & Engineering
ISBN: 9333223584

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.

Applied Laplace Transforms and z-Transforms for Scientists and Engineers

Applied Laplace Transforms and z-Transforms for Scientists and Engineers
Author: Urs Graf
Publisher: Birkhäuser
Total Pages: 501
Release: 2012-12-06
Genre: Mathematics
ISBN: 303487846X

The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications.

A Student's Guide to Fourier Transforms

A Student's Guide to Fourier Transforms
Author: John Francis James
Publisher: Cambridge University Press
Total Pages: 156
Release: 2002-09-19
Genre: Mathematics
ISBN: 9780521004282

Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.