Product Description
This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications. ... Read more

Customer Reviews (3)

Good, concise treatment
One reviewer characterized this book as little more than class notes.It is much better than that.It is, however, concise; the authors cover a lot of ground in few pages.As usual for graduate courses, a lot is required of the student.A good foundation in real analysis is assumed.For example, the authors say that Lebesgue's Dominated Convergence Theorem is beyond the scope of the book.This suggests that it is a more advanced topic, while really it is a less advanced topic that ought to have been covered in a prior course.In general, the book could be amplified to two or three times its length without taking up additional topics.I would not say that there are too few exercises, but it is true that a complete working out of the exercises in the back of the book would have been good.

Excellent book
I think this is an excellent book on Fourier series and Fourier transforms. I think their style is clear, concise and informative.

For example their treatment of pointwise conergence is explained in far simpler way then in other text.

The book is well done.

Little more than class notes...POOR class notes.
It appears that well-written advanced mathematics texts are few and far in between."Fourier Series and Integral Transforms" is no exception.The authors belie their goal in the preface, stating that the "aim of this book is to provide ... important examples of useful series of functions." They admit that this text was a bundling of class notes from a course of the same name, but do not specify who actually gave the course.After reading the first few chapters, I'm forced to conclude that either the authors have little experience in writing comprehensive texts or they do not know the material.

I'll say one nice thing before I rip into this: the price.When all of my other science books cost a minimum of $100 each, it is nice to only have to fork out $... for a book.

One axiom that holds true in all mathematics courses is that the way to quickly master the material is to work problems.It goes without saying that rote problem working without feedback serves no purpose but to burn trees and waste time.This is the crux of the problem that I have with this book: inadequate number of problems, no problem key and no examples in the book.

The number of problems in the book is sparse at best, and most aspects of the ideas in the text seem underrepresented in the problems.

The lack of a problem key means that when the student is working the problems she has no idea if she got it correct.Doing a problem wrong serves no purpose whatsoever, except to demoralize the student.Providing a key does not allow students to "cheat" as it were, since one needs to demonstrate the steps toward getting the answer.

Finally, there are "examples" in the book, but the majority of them end abruptly with the sentence "it is not difficult to show~" or "it is easy to verify~."
This is fine and dandy if there were enough complete examples to get you going.Unfortunately, there are not.I would expect this sort of thing from someone who slept through the actual class, then-faced with a publishing deadline-was forced to "finish" his book quickly.

My recommendation: if you have the choice-don't bother.If you are forced to purchase this book (i.e., required reading for signal analysis), then buy it used or better yet get it from the library.Sell it back as quickly as possible, because once someone else realizes that there is money to be made in writing (and selling) well-written signal analysis texts, this one will end up with no resale value whatsoever. ... Read more

Product Description
This book does what few books on integral transforms do: it constructs the kernels of the integral transforms by solving the generalized Sturm-Liouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and then use them to solve elementary problems of mathematical physics. This section, which proceeds mainly by examples and includes exercises, requires little mathematical background and provides an introduction to the subject of integral transforms. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed more at graduate students and researchers. Because of the applications it discusses, the book will interest engineers (especially petroleum engineers) and physicists. ... Read more

Product Description
Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises.

The most significant changes in the second edition include:

Product Description
This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics. ... Read more

Customer Reviews (3)

No details, impossible to learn from
This book covers a huge range of topics.There are no details.I am unable to work the homework problems with the details provided in the text.I'm googling information and will purchase a few more textbooks so I can learn something.This book might be good as a reference book if you already know what you're doing.

new chap 19 on numerical inverse laplace transforms
Chapter 19 is an excellent modern review of the main numerical inverse Laplace transform methods in use today.It does a good job of tying together many of the methods into a unifyingtheoretical light.Pretty much the only modern review out there, it was written by Dr John Knight, who is a co-author of one of the more important numerical inverse methods (Fourier series method of de Hoog, Knight & Stokes).

The rest of the book is great too.

Great Introduction
This well written book teaches by example and will quickly make youproficient in the subject. Davies uses complex analysis to approach thesubject which provides a way to visualize the problems. ... Read more

Product Description
An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided. ... Read more

Product Description
Integral transform methods provide effective ways to solve a variety of problems arising in the engineering, optical, and physical sciences. Suitable as a self-study for practicing engineers and applied mathematicians and as a textbook in graduate-level courses in optics, engineering sciences, physics, and mathematics.

Contents

- Preface
- Introduction
- Special Functions
- Fourier Integrals and Fourier Transforms
- Applications Involving Fourier Transforms
- The Laplace Transformation
- Applications Involving Laplace Transforms
- The Mellin Transform
- The Hankel Transform
- Finite Transforms
- Discrete Transforms
- Bibliography
- Appendix A: Review of Complex Variables
- Appendix B: Table of Fourier Transforms
- Appendix c: Table of Laplace Transforms
- Index ... Read more

Product Description
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener–Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. With 300 additional pages, this edition covers much more material than its predecessor.

New to the Second Edition

•          New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions

•          More than 400 new equations with exact solutions

•          New chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs

•          Additional examples for illustrative purposes

To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations. ... Read more

Customer Reviews (4)

It is a unique book!
This is an outstanding work, devoted to integral equations (linear and nonlinear), can be considered as a unique book: it contains a vast number of integral equations (>2500!!!) with corresponding analytical solutions (including new author's results) and a large collection of solving methods (analytical and numerical) appropriate for a given class of integral equations with illustrative examples.

Book recommended for modelling research
I am a chemical and petroleum engineer modelling flow in porous media. This book was extremelly useful for me to formulate flow problems allowing for analytical solutions.
Sicerely
Dr Carageorgos

Excellent book for engineering scientists
The book is highly recommended for engineers who use analytical models. The book contains several explicit formula and solutions allowing to avoid cumbersome numerical calculations. This feature is particularly important for solution of inverse problems, adjustment of the model to the data, for optimization, where solution of forward problem is used in algorithms for numerous times.

Sincerely,
Prof. Pavel Bedrikovetsky

Saved me a lot of time
I'm not a mathematician nor do I have many mathematician friends, but working on queueing theory during my master degree I started dealing with a bunch of integral equations. This book saved me weeks of looking around and reading to find the solution to Integral Equations that may or may not have a closed form solution. ... Read more

Product Description

This textbook presents an introduction to generalized functions through Sato's hyperfunctions, i.e. based on complex variables theory. Laplace transforms, Fourier transforms, Hilbert transforms, Mellin tranforms and Hankel transforms of hyperfunctions and ordinary functions are then treated, and some applications mainly to integral equations are presented. The book is written from an applied and computational point of view and contains many concrete examples.

Product Description
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians andengineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of researchand includes important results from other works.
With a description in Chapter 1 of foundational, topological information for the study of the distributions (generalized functions) andultradistributions to be considered, including the structure of these distributions, the author then moves on to an analysis of the transforms and ends with a discussion of the eigenfunction expansion of generalized functions. Applications of the transforms to various mathematical, physical, andengineering problems are given, and open research problems present a challenge to the reader. An extensi ... Read more

Product Description

This book gives background material on the theory of Laplace transforms, together with a fairly 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. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.

Product Description
The fourth and fifth volumes of this extensive multivolume project Integrals and Series are devoted to tables of Laplace transforms. In these companion volumes the authors have collected data scattered throughout the literature, and have augmented this material with many unpublished results obtained in their own research. Volume 4 contains tables of direct Laplace transforms, a number of which are expressed in terms of the Meijer G-function. When combined with the table of special cases, these formulae can be used to obtain Laplace transforms of numerous elementary functions of mathematical physics. Volume 5 offers tables of inversion formulae for the Laplace transformation and includes tables of factorization and inversion of various integral transforms. ... Read more

Product Description
Provides a mathematically rigorous, yet readily accessible treatment of applications of Laplace transforms.Includes the Dirac delta function given a completely justifiable treatment in the context of the Riemann-Stieltjes integral. DLC: Laplace transformation. ... Read more

Customer Reviews (4)

Undergraduate?
Just once, I'd like to pick up a math text that delivers the basics up-to and including the point of the book.This "undergraduate" book requires prior knowledge and didn't work for me as a self-teach, even with my 5-semesters of calculus.Very disappointed.

The Laplace Transform
The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Joel Schiff has demonstrated on a number of occasions that he is a master expositor of Mathematics and the current volume has to be among Dr Schiff's finest. 'The Laplace Transform' is an excellent starting point for those who want to master the application of transform techniques to boundary value problems and thus provides a backdrop to Davies' Integral Transforms and Duffy's Transform Methods.

Dr Schiff is to be particularly commended for his treatment of the inverse Laplace transform, which often receives scant attention in engineering texts.

Dr Schiff's book can be read at several levels; readers less interested in mastering the proofs may be interested to note that most of the standard transforms one meets in practice are covered either in the text or in exercises.

In sum, 'The Laplace Transform' is for those who want to get beyond the 'operational technique' status of the method, and is strongly recommended to readers who have covered a first course in complex variables. It should appeal to Mathematicians and Engineers alike.

Well Written and Presented
I thought this book was really well written and presented. It has really helped with my understanding of Laplace Transforms. I would highly recommend this book to engineers who want a deeper understanding of transforms. It is worth while reading up on Residue Theory and Cauchys Theorem before reading this book. I am sure that I will constantly reference back to this book for my work.

I like this book
This book is written in a very clear style, suitable for self-study. The exercises have been well chosen and correctly placed. It might be most effective if read concurrently or immediately after an elementary course onDifferential Equations at the level of Zill's book. Teachers should take alook at this book, it shows how to deal with the subject rigorously withoutbeing boring. No measure theory is required. ... Read more

Product Description
An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained. ... Read more

Product Description
This book, which grew out of lectures given over the course of several years at Kharkov University for students in the Faculty of Mechanics and Mathematics, is devoted to classical integral transforms, principally the Fourier transform, and their applications. The author develops the general theory of the Fourier transform for the space $L^1(E_n)$ of integrable functions of $n$ variables. His proof of the inversion theorem is based on the general Bochner theorem on integral transforms, a theorem having other applications within the subject area of the book. The author also covers Fourier-Plancherel theory in $L^2(E_n)$. In addition to the general theory of integral transforms, connections are established with other areas of mathematical analysis--such as the theory of harmonic and analytic functions, the theory of orthogonal polynomials, and the moment problem--as well as to mathematical physics. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's large-scale digitization efforts. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the original text that can be both accessed online and used to create new print copies. The Library also understands and values the usefulness of print and makes reprints available to the public whenever possible. This book and hundreds of thousands of others can be found in the HathiTrust, an archive of the digitized collections of many great research libraries. For access to the University of Michigan Library's digital collections, please see http://www.lib.umich.edu and for information about the HathiTrust, please visit http://www.hathitrust.org ... Read more