Book Description
This book proveds a clear, concise explanation of Laplace transforms, or operational calculus--now necessary knowledge for engineers, physicists, mathematicians and other scientists. Definitions, principles and theorems are illustrated and reinforced by hundreds of fully worked out problems. Also included are chapters on complex variable theory and Fourier series and integrals, so important to discussions of the complex inversion formula.
Customer Reviews:
Laplace Transforms.......2007-05-12
I have several books on Laplace Transforms; but the Schaum's Outline by Murray Spiegel is particularly well done. The book is logically organized with many worked out examples. This is a classic overview of the Laplace Transform.
Not for us.......2007-05-01
Not for people who need a book on Laplace Transforms. Yes, lots of practice problems with answers. If you get lost and don't know how to go about a problem well page reference would have been nice.
Learning.......2007-01-06
Good overall coverage. nice explanations, and worked examples. id recommend it to anyone wanting to brush up on their transforms before an exam.
Laplace Transforms Explained in Plain English.......2005-09-23
This is a valuable reference to keep handy as a reminder about which transform methods best apply to various problems that you need to solve around the office.
It helped me through control systems.......2003-12-29
This book taught me both the basics and some of the finer points of LaPlace Transforms to get me past that hurdle so that I could begin focussing on the actual material presented in my BioControl Systems course. Many people got so caught up on the mathematics of LaPlace Transforms that they did not even get to the point where they could begin understanding control systems. I bought this book from Amazon at the beginning of the semester and it turned out to be a life-saver for me. I think that had I not sat down with this book for a weekend and taught myself LaPlace Transforms, I would have not passed that class.
Granted, this is a single case for a single class of a single bioengineering student; nevertheless, for my part I strongly recommend this book. I was put in a class where the teacher expected the students to have an understanding of the mathematics from the start. The majority of us didn't have that background, and this book clearly, simply, and without too much complication prepared me for my class which was exactly what I wanted it to do. It has been one of the best investments (as far as school books go) of my college career.
I must leave you with one parting word of wisdom. This book, and I don't think any other book dealing with such an advanced topic, is not easy to read. You will not be able to thoughtlessly master the material. You will work to understand it; your brain may hurt at times. But this book presented the information in a much-more-easy-to-digest manner than any of my college math textbooks, and for that, I am grateful.
Book Description
Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.
Customer Reviews:
Excellent.......2003-11-08
This book is quite thorough, but remains easy to follow (considering the material). It starts out with partial differential equations (no previous PDE experience needed) and shows where Fourier series comes from, which I found motivating since the purpose of Fourier Analysis was evident from the beginning. It then goes into making solutions of arbitrary functions out of sine and cosine functions as well as touching on other orthogonal sets.
The book's main focus is on starting with PDEs and ending with a solution of a Fourier series.
The first chapter was the hardest since the approaches to problems were much different than in calculus, but after adjusting to the material and the approaches to the problems, it gets easier!
Great text for an intro to pde's course!.......2003-04-30
My first encounter with partial differential equations was out of this book. Since then, I've had another course on pde's, and used this book as a reference quite often. Fourier Series adn Boundary Value Problems is very much like Complex Variables and Applicatoins, also by Churchill and Brown. It's accessible to a large audience. Though it would help to have had an advanced calculus course, it isn't necessary to understand the mechanics of solving pde's (namely the variables seperable cases, which is mostly what's in this book). If you're an undergraduate math, engineering or physics student, you'll probably be using this book.
Try Another Text.......2000-08-23
I found Dr. Brown, in conjunction with Dr. Churchill, to have written a very dry and non-useful text. It fails to provide the undergraduate student with the resources and background information that more highly touted books offer. There are a few examples that are somewhat helpful, but overall I found myself having to use reference texts to supplement this one. I am not a math major, but am continually searching for good math texts to help me grasp the fundamentals of more difficult topics. I did not find that help here. Too much 'math prose' and not enough to-the-point definitions and examples, which is the cry of every non-math major. Their treatment of the Laplacian is not even worth the bother of placing it in the book. The physical size of the book is small, (9 1/2 by 6") with 335 pages. Not nearly enough for the treatment of its titled subject.
An excellent book on Fourier Series.......2000-02-12
This is a great book that gives precise examples which are easy to comprehend. Dr. Brown proves to be an excellent author once again.
Customer Reviews:
DSP Bible.......2000-04-04
Written by one of the biggest DSPs Gurus. I can say that this book is my bible on DSP, it toke me some time to understand some parts of the book, but this i due to the huge amount of knowledge present on it. Best description "Open Minder"...
Average customer rating:
- Good, concise treatment
- Excellent book
- Little more than class notes...POOR class notes.
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Fourier Series and Integral Transforms
Allan Pinkus , and
Samy Zafrany
Manufacturer: Cambridge University Press
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ASIN: 0521597714 |
Book 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.
Customer Reviews:
Good, concise treatment.......2007-05-02
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.......2004-03-07
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........2002-02-04
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.
Book Description
Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.
Customer Reviews:
so-so.......2004-12-21
This book was my first contact with measure theory. I read this for self study -- more or less as a leisure book. The material is aimed at undergrads, and probably doesn't assume much past plain ol' college calculus. However, the more you know, the easier it will be to read. Any experience with analysis, and proofs will be helpful. And, in chapter 7, "Function Spaces", a linear algebra course will come in very handy.
Anyway, it's not a hard book to read, but it is very dry. Because the book is so short, there is not much room for anything other than a list of definitions, lemmas and theorems. There isn't really much insight. All the way through chapter 7 I was basically plodding along, simply because I wanted to finish the book. However, I'm glad that I did, because I found chapter 8 really fascinating. I think this chapter (Fourier Series in L^2) really ties the book together because you get to see measure theory and lebesgue integration working in harmony with linear algebra. I never really liked linear algebra that much until I read this chapter.
Unfortunately, chapter 9 was a let down and I actually quit reading a few pages before the end of the book. I had already got what I needed out of it. It's a good intro to measure theory if you just want to see what it is, and not really go into detail with it. A lot of the lemmas, propositions and corollaries are left as exercises. I tried to do a handful of problems from every chapter, especially the ones that fill in the text, and had little or no difficulty with any of them.
I would have given this 3 stars if not for chapter 8. For the price, I would recommend it, especially if you love calculus, but never liked linear algebra, because it will hopefully tie them together for you. Now I can't get enough linear algebra! I know, it's sick ;) Then, with your newfound love of linear algebra, read Hubbard and Hubbard's _Vector_Calculus,_Linear_Algebra,_and_Differential_Forms:_A Unified_Approach_, which is currently blowing my mind :)
Good review of Lebesque integration.......2004-11-24
This is more about Lebesgue integration, covered in the first 112 of 154 pages, than about Fourier Series. But do not be fooled by the low price; this book makes for very good review of the Lebesgue theory, well organized and concise. Or with moderate mathematical maturity, the reader could learn the theory here.
Gentle Intro to Measure Theory.......2002-04-04
I am using this book with two advanced undergraduates, after working through a basic introduction to analysis text the previous semester. Each section is about 3 or 4 pages long, giving the main results and most proofs, although some are left as exercises. Each chapter ends with a nice set of exercises, most of which are accessible to students who feel comfortable with epsilon/delta proofs. The book is very short and concise, 145 pages plus an appendix summarizing basic analysis results on sets, countability, functions, and sequences.
Chapter 1 reviews the Riemann integral and some of its drawbacks. Chapter 2 introduces the idea of outer measure and measurable sets, all on the unit interval. The next two chapters discuss properties of measurable sets and measurable functions. Chapters 5 and 6 then cover the Lebesgue integral and convergence theorems. The last three chapers introduce L2 spaces, Fourier series, and proofs of convergence.
All in all this is a good, very cheap way to learn the basics of measure theory and the Lebesgue integral, before moving on to something like Rudin or Royden.
direct intuitive treatment but much "left as an exercise".......2000-11-09
This assumes some advanced calculus and then introduces enough Lebesgue integration amd measure theory to explain and prove the basic convergence results for (generalized) Fourier analysis. Second half of second year and above.
Everything is very well motivated and the book is not long, but quite a lot is "left as an exercise for the reader." This really hurts the book for self study in my view. If you have a bigger book on real analysis and want another treatment, or need a refresher this will do nicely. On its own -- you've been warned.
A good basic introduction to Lebesgue integration.......2000-06-12
A good basic introduction to Lebesgue integration, but a little sketchy in some places. Each chapter concludes with a good set of exercises. This book is good for getting the "idea" behind Lebesgue integration, but comes up short on many of the details. An excellent companion volume would be Jones' "Lebesgue Integration on Euclidean space".
Book Description
A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley begins with a physical problem and applies the results to different situations. 1966 edition.
Customer Reviews:
best intro to fourier series and fourier transforms ever.......2005-11-01
Starts with the Dirichlet problem to physically motivate Fourier series. Works out the basic theory of Fourier series (Poisson, Dirichlet kernels, etc.). Then moves onto the line---again with physical motivation---and Fourier transforms, and analyzes the time-dependent heat equation.
Saved my life in grad school.
Customer Reviews:
Good for Review.......2002-10-31
Like the other books of the Schaum's Outline series, this book goes through the theories and shows you how to work the problems step by step. Although this is very helpful, I like to be able to test my knowledge. I say this is good for review because you will remember as you read this. You will also have a good idea of whether you are doing the supplementary problems correct or not. Here, most the supplementary problems do not have answers. Those that do, just have the final answer rather than an illustration of how the writers got the answer. This is difficult if you are learning about real variables for the first time.
As well as giving you the basic concepts, this book also goes into Lebesgue integrals, Riemann integrals, and Fourier series. The explanations are fairly well written, and the examples are easy to follow.
Book Description
The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics.
Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.
Customer Reviews:
Excellent collection of diverse examples.......2000-06-07
If you want a diverse collection of examples of the many different kinds of applications of the theory of Fourier series and Fourier integrals, you could hardly do better than this book. These include not only wave motion and heat flow (covered in every textbook), but also: the central limit theorem, the geometry of numbers, the isoperimetric problem, Heisenberg's inequality, recurrence of random walks, quadratic reciprocity, and many others.
(This book also explains the theory of measure and integration from scratch, but do not assume that this is the best place to learn that subject for the first time; the treatment of that topic is rather terse.)
Book Description
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of Münz and Szász concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form $\sum^N_1A_ne^{i\lambda_nx}$, lacunary series, generalized harmonic analysis in the complex domain, the zeros of random functions, and many others.
Average customer rating:
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Analyse mathématique II: Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes
Roger Godement
Manufacturer: Springer
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ASIN: 3540006559 |
Book Description
Les deux premiers sont consacrés aux fonctions dans R ou C, y compris la théorie élémentaire des séries et intégrales de Fourier et une partie de celle des fonctions holomorphes. L'exposé non strictement linéaire, combine indications historiques et raisonnements rigoureux. Il montre la diversité des voies d'accès aux principaux résultats afin de familiariser le lecteur avec les méthodes de raisonnement et idées fondamentales plutôt qu'avec les techniques de calcul, point de vue utile aussi aux personnes travaillant seules.
Les volumes 3 et 4 traitent principalement des fonctions analytiques (théorie de Cauchy, théorie analytique des nombres et fonctions modulaires), ainsi que du calcul différentiel sur les variétés, avec un exposé de l'intégrale de Lebesgue, en suivant d'assez près le célèbre cours donné longtemps par l'auteur à l'Université Paris 7.
On reconnaîtra dans ce nouvel ouvrage le style inimitable de l'auteur, et pas seulement par son refus de l'écriture condensée en usage dans ce nombreux manuels.
Books:
- Schaum's Outline of Operations Research
- Schaum's Outline of Partial Differential Equations (Schaum's)
- Scientific Computing
- Scientific Computing
- Scientific Computing
- Scientific Computing
- Statistical Abstract of the United States 2007 (Hardcover): The National Data Book (Statistical Abstract of the United States)
- Successful Scientific Writing: A Step-By-step Guide for Biomedical Scientists
- Systems Thinking, Systems Practice: Includes a 30-Year Retrospective
- The Colours of Infinity: The Beauty, The Power and the Sense of Fractals
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