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Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics)
Mark A. Pinsky
Manufacturer: Brooks Cole
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ASIN: 0534376606 |
Book Description
Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, several different proofs are offered for a given proposition, allowing readers to compare different methods.
Customer Reviews:
For the Students!.......2002-07-23
Courses in harmonic analysis have a central place in the course offerings of every math department, be it pure or applied;-- and the subject is as important as ever! Yet it has not always been easy for an instructor to find a book that is right for the students. Some books might be too skimpy on proofs, or not deep enough.-- Or the applications may somehow be artificial, or contrived. Afterall, we teach the material to engineers!-- It is a relief to find, in Pinsky's lovely new book, a balanced approach to the subject. The motivation and the history receive a beautiful presentation, as do the technical points and proofs. And the historical comments- sprinkled throughout the book- bring the subject to life. At the same time, the book is forward looking, and it has been tested in courses. Great exercises! The structure of the exposition is friendly, and gently leads the reader toward the exciting new wavelet material in the last hundred or so pages of the book. The student thereby gets a sense of how the central questions in wavelet theory have their root in the more classical ideas of harmonic analysis.
Book Description
From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)
Customer Reviews:
a superb book.......2006-04-05
This is a rewrite of the great book by Courant, and it does justice to its origin. I prefer the somewhat more charming original book of Courant myself, but I have taught from this one too and learned something more.
Since the original Courant costs $120 for the 2 volume set, this volume at $33 is a bargain, so snap it up. This is 10 times as valuable as most current $130 calculus books.
More than an introduction.......2005-12-15
Those books (volumes 1-2) can be seen as a new edition of Courant's classical Differential and Integral Calculus, volumes 1-2 (that can still be used for general calculus courses). The first volume was written while Courant was still alive, and the second was postumous. I believe that they are the best work to start understanding analysis. Indeed, for the general scientist (as a physicist) it contains all the theory needed for any application. The book is not easy reading though. Much of the text can be understood on first reading, but there are pretty profound sections, mostly on the appendixes, that turn the book genuinely onto a book of analysis. The second volume requires some mathematical maturity, and I doubt whether it is suitable for beginners, but it is simply the best book of multivariate calculus that I know - and it is really difficult to think of a better presentation. Courant was a giant, and his concept of mathematics shines in every page of those books (although he did not see the publication of the second volume, his hand can be seen in every page). For the serious mathematician, a must-have. For the beginner, the best way to get in love. Courant and John don't lie, they give every proof and guide you most gently in this complicated garden called mathematics. I'd give it aleph stars if it was possible.
Absolutely beautiful!.......2005-01-24
I give 5 stars to this book because in contrast with the majority of the calculus textbooks it gives the reader the perfect combination between rigor and intuiton. Another thing that I also like a lot is the fact that volume 2 has solutions to almost all the excercises, which is great because some of the problems are very difficult. I really think this book is a "must have".
simply the Best Calculus Book.......2002-08-12
An intuitive, rigorous and a beautifully conceptual approach to calculus is what distinguishes this book from the thousands of run-of-the-mill "Calculus I" textbooks published every year.
This is not surprising because 1) Courant and John were both important German-born mathematicians, both schooled in that great mathematical mecca, Gottingen, both making fundamental contributions to many classical branches of pure and applied mathematics. Courant is an especially important mathematician since he not only studied under the greats Minkowski and Hilbert - even serving as the latter's assistant - but founded the Courant Institute of Mathematical Sciences in New York, modelled on the Gottingen Mathematical Institute. 2) That typical German thoroughness and emphasis on the mastery of the "fundamental concepts", so dear to German textbooks, is evident in all sections of the book, particularly in the introductory material on the number continuum, functions, continuity etc.
The exercises at the end of chapters are substantial and excellent, and help to develop proof skills in students as well as a subtle mathematical intuition.
Mathematics is best learnt by studying books written by important mathematicians. Classic books like these should always serve to prove the truth of Abel's dictum that to master mathematics one should 'study the masters and not the pupils'.
You must have this........2002-05-28
My review of the first volume pretty much applies here as well. How many *calculus* texts have an introduction to complex variables, and the theory of analytic functions? This is the only one I've ever seen, and I don't think anyone else could make it more enriching than Courant. Useful material on vector calculus, the theory of matrices, and even introductory material on the *calculus of variations* (something we usually don't see at *all* in the undergrad curriculum) is included. It is refreshing to have an instructor like Courant, who doesn't assume we can't follow higher mathematical roads, but also doesn't sit at the other end of the spectrum, just waving a wand and "poof, here is the result".
Courant also published a standard reference work (also two volumes, I believe) on Mathematical Physics. While the level of mathematics required is post-grad, I was still able to read sizeable sections of it without getting lost.
We can only hope Dover decides to publish Courant's works one day, to make them a little more affordable. But still, you can buy both volumes of Courant's intro to calculus for about the same price as a modern calculus text that waters down the material, and on top of that, provides inadequate explanation for the material it does cover.
Book Description
A new, revised edition of a yet unrivaled work on frequency domain analysis
Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition:
- Devotes an entire chapter to complex demodulation
- Treats harmonic regression in two separate chapters
- Features a more succinct discussion of the fast Fourier transform
- Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility
- Includes Web addresses for all time series data used in the examples
An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.
Customer Reviews:
nice beginning treatment of frequency domain time series.......2001-07-01
As a time series analyst who studied time series in graduate school when the first edition of Bloomfield's book came out, I really appreciated it. The frequency approach to time series is not natural because we tend to look at the series to see how it changes (fluctuates) over time. This makes the time domain approach very natural. It is only when one sees periodicity in the series and can relate the series to a summation of sine and cosine waves that the frequency domain ideas get appreciated.
Bloomfield introduces Fourier series in a gentle way, making it clear. Concepts are introduced as needed to deal with specific aspects of real time series data. I particularly liked his treatment of complex demodulation, which could be a very difficult concept to grasp if not presented carefully. But Bloomfield explains it well and provides another way to look at the famous Wolfer sunspot data using an approach based on complex demodulation (assuming a slowly changing period for the series).
Book Description
This book is a self-contained introduction to Laplace Transforms and Fourier Series; emphasising the applications of Laplace transforms throughout, the book also provides coverage of the underlying pure mathematical structures. Alongside the Laplace transform, the notion of Fourier series is developed from first principles. Exercises are provided to consolidate understanding of the concepts and techniques, and only a knowledge of elementary calculus and trigonometry is assumed. For second and third year students looking for a rigorous and practical introduction to the subject, this book will be an invaluable source.
Customer Reviews:
excellent text.......2005-09-20
This is an ideal introduction for mathematicians and applied scientists. Written in an easy to understand style and full of good relevant examples. I guess only the more mathematical will be able to digest the last chapter.
All exercises have not only answers but solutions which students will appreciate.
Clearly written introduction.......2000-01-02
This textbook tries to strike a balance between the "toolkit" (how to use it) approach (supposedly) desired by engineers and the more rigorous mathematician's development. Speaking as an engineer, I found it not as intuitive as I had hoped (I'm more mathematically-oriented than most engineers) However, the book is clearly written and develops the arguments in small steps. Recommend it as helpful, but perhaps supplemented by more careful development.
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An Introduction to Nonharmonic Fourier Series
Robert M. Young
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover
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ASIN: 0127729550 |
Book Description
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.
Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Book Description
This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical techniques is required; the book is suitable for advanced university students, and can be used as the basis of a short undergraduate lecture course. A valuable and original feature of the book is the use of generalised-function theory to derive a simple, widely applicable method of obtaining asymptotic expressions for Fourier transforms and Fourier coefficients.
Customer Reviews:
Great for self study.......2007-08-05
Nice little book. Concise and clear. In the typical English style, many of the proofs are left to the reader. Lighhill will assume what he finds obvious is also obvious to the reader. This was not always the case for me. He does this alot in the proving theorems so have a pencil ready. It is alot fun to work through the proofs becuase he gives rough sketches and leaves you to fill in the details. He manages this without loss of clarity or rigor. It is good pedagogy for anyone familiar with basic analysis of real variables and some knowledge of complex variables.
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.
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Fourier Series and Optical Transform Techniques in Contemporary Optics: An Introduction
Raymond G. Wilson
Manufacturer: Wiley-Interscience
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Binding: Hardcover
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ASIN: 0471303577 |
Book Description
Fourier Series and Optical Transform Techniques in Contemporary Optics
An Introduction
For anyone new to Fourier methods, this remarkable book will illuminate the subject like no other currently available. With over 280 illustrations generated by computer graphics, it depicts in 3-space (rather than the usual 2-space) the many basic functions of optical diffraction and imaging. These mind-stretching visualizations give the reader an enhanced understanding of both Fourier transform techniques and key principles in optics. At the same time, the author provides a lucid text that covers wave notation, the Fourier analysis of signals, the processing of light in diffraction phenomena and imaging, Zernicke polynomials, Fourier transforms for Fresnel diffraction, laser beacon adaptive optics, and related topics.
Ideal for self-teaching, this book is highly recommended for working engineers, technical staff, students of physical optics and signal analysis, and Fourier novices in all fields.
Book Description
The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the field. All the material has been update and several new sections explore the recent progress made in the areas of wavelength modulation, analog information processing, and holography. The book also explores Fourier analysis applications and emphasizes those applications to diffraction, imaging, optical data processing, and holography.
Customer Reviews:
Simply the best.......2007-07-11
Only the best will do - and this is it.
Mandatory reading for anyone involved in optics. Goodman's books are treasure troves.
A very nice book , but nothing is ever perfect..........2005-10-07
Overall I like the book for it is clear, the mathematics is lucid and has all the essentials in a comprehensive way. I have found it quite useful for research. In addition, for the most parts it is quite accurate.
Some criticisms though:
Contains everything from a more mathematical point of view. By that i mean, problems are usually not very physically motivated and some of the conclusions drawn are not very physical. that is you are given at the end of a discussion only an integral. It would have been nice if there were more discussions on the physics of Fourier Optics, for example pictures of actual experimental results or clear diagrams that show for example how does the diffraction pattern for a given input looks like. So getting an intuitive grasp of the subject at a pictorial level, where you can 'see' the results is a bit challenging to get out of this book. also very expensive.
Goodman's Fourier Optics 3rd Edition: An Improved Classic........2005-08-12
For the last month, I have been using this book for self study to aid me in my work with lasers. Originally, I was working from the 1st edition (borrowed from a co-worker), but decided to buy my own copy. I wound up buying the 3rd edition, a significantly expanded version of the original.
Goodman's writing style is conversational and his treatment of the subject is thorough. I appreciate his inclusion of enough optics/E&M background within the text that I am not constantly having to go to my bookshelf to consult other references. Note, the 3rd edition has several helpful appendices not found in the 1st edition.
There are also many instructive problems given throughout the text to help students solidify their understanding of the material.
This is an excellent book for self study, and would certainly make a fine text for a senior undergrad course on the subject. I recommend it highly.
Charlie.
The best book on the topic.......2005-07-14
This is the best book on Fourier Optics that I'm aware of. There is sufficient detail that you can follow the math, but also has well written text explaining concepts. The problems are sometimes trivial and sometime challenging, but they are very much an integral part of the book and doing them is necessary to get a full understanding of the material. There is a 3rd edition of the book with an additonal chapter, which is available at a much lower price, but Amazon does not seem to be carrying it yet. Hopefully they will soon. (...)
A good path to physical optics and imaging theory.......2000-06-14
This book is cleary written. The basic theory of Fourier transform is included too. Fourier optics is a very strong tool in imaging and optics. I would say Goodman is an enginnering guy, but some physical insight is not very clear. Diffraction theory is easier to understand than J.D. Jackson's E&M. And the whole book is easier to read than Born and Wolf's Principle of Optics and has more details. After all, it is a good book for Fourier opitcs. But the price is too high.
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