Book Description

The book presents a modern theory of holomorphic function spaces in the open unit ball. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing proofs in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group.

Book Description

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDE's, probability, diffraction, musical tones, and wavelets. Providing unified development of (univariate) Fourier analysis for functions on R, T, Z, and P, the book also includes an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. It also uses the FT calculus and generalized functions to study the (univariate) wave equation, diffusion equation, and diffraction equation. In addition, fine points of the theory are developed. The book also demonstrates real-world applications of Fourier analysis in the chapter on musical tones.A valuable reference on Fourier analysis for a variety of scientific professionals, including Mathematicians, Physicists, Chemists, Geologists, Electrical Engineers, Mechanical Engineers, and others. ... Read more

Reviews (2)

Elegant, Sophisticated Math, Great Examples & Problems
I am taking this class as an undergraduate course with Dr. Healy at University of Maryland at College Park. This is an elegant, thoughtful book that provides a rich math course that is a welcome alternative to run-of-the mill engineering math classes lacking in intangible qualities. Many of the problems are tough and require some rigorous math at an advanced, math-major level (real analysis would be helpful) but are overall accessible to engineering seniors with strong math skills and office hours support from the professor, and the problems are well-geared to illustrating and exploring the topics in the text. As another benefit to the student, the examples definitely help one warm up for the problem solving at the end of the chapters. In addition to the richness and elegance of the subject as presented, this is a thoughtfully constructed and presented text.

The first several chapters introduce fourier transforms and related math such as convolutions as a set of operations in a variety of spaces, including continuous, discrete and periodic spaces. Then the text goes into the theory of distributions/generalized functions and solutions of differential equations. Several additional chapters take the subject into wavelets. The presentation of the Fourier transforms having a variety of manifestations in different kinds of spaces unifies in a fundamentally harmonious (no pun intended!) and beautiful way the disjoint and arbitrary Fourier processing taught to engineering undergraduates.

Moder Approach, Good Balance between Theory & Applications
I have been interested in the Mathematics of Fourier Series/Fourier Transform methods for well over 15 years. I own already well over 10 books on this subject. The book by David Kammler strikes me as having a particularly good balance between theory and applications as well as taking a modern computer approach to this ever relevant subject. Important topics such as sampling theory and the Fast Fourier Transform (FFT) are well covered and explained in detail. Also, chapters that apply Fourier Analysis to important physical areas (heat conduction, light diffraction, wave propagation, musical sound, etc.) illustrate and higlight the relevance of Fourier Methods in the real worls. There is also a nice summary at the end of the book that explains the histoy and most important application of Fourier Analyis (very nice). Ample computer excerices and the traditional proof/derivation homework problems are included. The book also seems to prepare the reader well for the increasingly subject of Wavelets and applying them musical sound. Also, what makes the book stand out from more traditional ones is the emphasis on Numerical Method and using the computer to solve or illustrate some of the powers of Fourier Analysis. Readers considering using this text should best have a background in calcus, differential equations and Matrix methods. This probably puts it at the junior/senior undergradudate level. 1st year graduate students might also benefit from the text.

In a nutshell this is an excellent textbook for anyone serious about Fourier Analysis and applying those methods via computer (or pencil) to real world situation. This is probably one of the best books yet on this very important subject. Highly Recommended! ... Read more

Book Description

A convenient single source for vital mathematical concepts, written by engineers and for engineers.

Builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs.

The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers:* Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory * Concise coverage of fundamental concepts such as sets, mappings, and linearity * Thorough discussion of topics such as distance, inner product, and orthogonality * Essentials of operator equations, theory of approximations, transform methods, and partial differential equationsIt makes an excellent companion to less general engineering texts and a useful reference for practitioners. ... Read more

Reviews (1)

A book for Advanced Engineers
As a student of the author, in which the book is used in a grad level engineering school, this book summarizes all that is learned in an under grad engineering college.Many mathematical aspects are considered from simple algebraic logic to advanced Fourier transforms.This book covers it all.In summary, this book is great to own if you are interested in combining all what is learned in mathematics to solve complex problems. ... Read more

Book Description

This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. A self-contained text, it presents the necessary background on the limit concept. (The first seven chapters could constitute a one-semester course on introduction to limits.) Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. More than 750 exercises help reinforce the material. 1981 ed. 34 Figures.
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Reviews (1)

Very good
Everybody seems to think that Rudin's Principles of Mathematical Analysis is the best for whatever reason, & I agree that it's good for reference after being exposed to the material. Pfaffenberger doesn't construct the real numbers using Dedekind cuts, he makes a list of 13 axioms that basically say that the reals is the only complete ordered field. I think I liked this approach better than Rudin's (or Hardy's) more abstract approach. He also spends much more time developing metric spaces (including the Baire Category Theorem & nowhere dense sets, etc, which Rudin omits except for a couple exercises) and the Riemann-Stieltjes Integral. Then there's a short chapter where transcendental functions exp, sin & cos are defined which I think Rudin skips, and then introduction to inner-product spaces. Fourier series is introduced in the chapter on general inner-iroduct spaces (with a first look at Banach Spaces as an aside) rather than the chapter on sequences & series of functions. I also liked this better than Rudin's text or other calculus texts. Rudin includes a whole chapter on functions of several variables, but Pfaffenberger doesn't have anything on them. Instead, there's a chapter on normed linear spaces and the Riesz Representation Theorem, and then similar to Rudin, a chapter on the Lesbesgue Integral. This book has many more problems than Rudin's or Apostol's, and in general they are a bit easier. Of course every section has its difficult ones but the first ones are almost always just "verify that blah blah is true". The last ones are about on the same level as the ones in Rudin's book. ... Read more

Book Description

June 23, 1993. A Princeton mathematician announces that he has unlocked, after thousands of unsuccessful attempts by others, the greatest mathematical riddle in the world. Dr. Wiles demonstrates to a group of stunned mathematicians that he has provided the proof of Fermat's Last Theorem (the equation x" + y" = z", where n is an integer greater than 2, has no solution in positive numbers), a problem that has confounded scholars for over 350 years.

Here in this brilliant new book, Marilyn vos Savant, the person with the highest recorded IQ in the world explains the mathematical underpinnings of Wiles's solution, discusses the history of Fermat's Last Theorem and other great math problems, and provides colorful stories of the great thinkers and amateurs who attempted to solve Fermat's puzzle.
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Reviews (34)

A review of these reviews
Ah, these poor little threatened egos on display:How dare anyone contradict the university professionals?How dare anyone have an opinion outside the status quo?How dare any publisher even consider a book not from a fully affiliated tenured and chaired professor of mathematics?Where is peer review when we need it?I especially enjoyed the brag of vandalism.Savonarola would be proud.

Im SO excited
Isn't it just marvelous, finally a chance to polish up my knowledge of the worlds most famous maths problem. I can't tell you how much me and my wife have enjoyed, and been entregued by this. Night-after-night, just laying down on the hay, having a laugh with this top quality piece of material. Maths world here I come.

A courageous woman
I browsed the book in bookstore and I immediately became disgusted. After I recovered, I started to think positive as I stared at the averagely-looking face of this amazing woman that she put alongside Fermat. There's something special about this woman, I must admit, as evidenced by her apparent success. She must be a good transmitter to exposit to her equals what she learns from her equals, which is, of course, abundant in numbers. I think she has that exact mean IQ to fit into the job perfectly. But, I cannot forgive her talk about FLT, or General relativity.

Excellent, honest book
This is a fantastic book!I especially like the fact that she highlights several problems with the current state of mathematics, drawing this field (and maybe all of modern science) into question.

Few people dare to question science, but Marilyn has done so, and she has good reason for it.If half of the scientists of the world were in politics, the world would be a much better place.Politics is in dire need of minds capable of flexible, yet rigorous thinking, and scientists are experts at this sort of thing.

Bravo, Marilyn!

One star because I can't give zero...
Marilyn should have quit while she was ahead (with the Monty Hall problem). If I were the person with the highest IQ in the world, I would have made sure that I understood at least the rudiments of mathematics and logic before writing a book about them. ... Read more

Book Description

The volume is based on the Sobolev-Schwartz concept of Generalized Functions. It presents general theory including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner, Poisson integral transforms and operational calculus.This volume also includes numerous problems, exercises, examples and figures. ... Read more

Book Description

Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by Professor Kac over the last few years at MIT.

FROM THE REVIEWS:

MATHEMATICAL REVIEWS "The authors have written a very accessible book. They have deviated from the classical approach and notation in a way that should prove quite successful." ... Read more

Book Description

During the past two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to better known computational procedures, such as finite difference and finite element methods of numerical solution, in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting.This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the author presents the subject using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments.This book will be of interest to graduate students, scientists, and engineers interested in applying pseudospectral methods to real problems. ... Read more

Reviews (1)

This is a guide, not an expository report
This book is a wonderful guide to pseudo-spectral techniques which begins its discussion as an extension or more precisely as the limit of finite difference techniques. Unfortunately for anyone who would wish to learn these techniques I would have to recomend another book. However, for someone who already knows these techniques then this book is invaluable. It covers in a clear, mathematical way in which certain pitfalls and problems may be overcome. It does not, however, teach more of the advanced methods that must be used in more complex boundary value problems.

I think that a mathematician will find this book easy reading. I also think that an educated engineer will also have little difficulty following along. I do not recomend this book to anyone who has not taken a course in PDE's as background theory is always more important to application than indiscriminately learning a technique. ... Read more

Book Description

Includes the NETSOLVE Software Package and User's Manual. ... Read more

Book Description

A comprehensive, up-to-date, and accessible introduction to the numerical solution of a large class of integral equations, this book builds an important foundation for the numerical analysis of these equations. It provides a general framework for the degenerate kernel, projection, and Nyström methods and includes an introduction to the numerical solution of boundary integral equations (also known as boundary element methods).It is an excellent resource for graduate students and researchers trying to solve integral equation problems and for engineers using boundary element methods. ... Read more

Reviews (1)

A Good Introductory Text at the Graduate Level
Atkinson's book is a good introduction of the material. The book is written is such a way that someone who is familiar with Galerkin finite element methods for partial differential equations can quickly gain someunderstanding of numerical methods for this class of integral equations. For a more complete review, see Ian Sloan's review in the March 1999 issueof SIAM Review. ... Read more

Book Description

Designed for the full-time analyst, physicists, engineer, or economist, this book attempts to provide its readers with most of the measure theory they will ever need. Given the choice, the author has consistently opted to develop the concrete rather than the abstract aspects of topics treated.

The major new feature of this third edition is the inclusion of a new chapter in which the author introduces the Fourier transform. In that Hermite functions play a central role in his treatment of Parseval's identity and the inversion formula, Stroock's approach bears greater resemblance to that adopted by Norbert Wiener than that used in most modern introductory texts. A second feature is that solutions to all problems are provided.

As a self-contained text, this book is excellent for both self-study and the classroom. ... Read more

Reviews (1)

A perfect place to start Real Analysis
This is a perfect textbook for a one-semester course in measure and integration at a graduate level. It's concise but complete and detailed, rigour but motivated and inspiring. It's more technical than Bartle's little book on integration. It also has solution manual in the end to check on. I hope more readers enjoy such a wonderful germ written by a star form MIT. ... Read more

Book Description

¿The author describes this marvelous book as designed for beginning graduate students in mathematics¿-in particular for those who intend to specialize in applied mathematics, and for graduate students in other disciplines such as engineering, physics and computer science. The first six chapters contain enough material for a year course, and the final two chapters contain related material¿ Those who are familiar with the author¿s earlier books will not be surprised by its excellence. It is businesslike and will be found to be demanding, but it is user-friendly. It is the reviewer¿s opinion that it will be extremely useful and popular as a text; institutions that do not already require their students to take such a course no longer have an excuse, and should immediately organize one based on this book.¿¿Mathematical Reviews ... Read more

Reviews (1)

Solid resource for the applied mathematician
Cheney's book is a good overview of the main topics in real and functional analysis, especially aimed at the applied mathematician. Don't be confused by the title - the book contains few examples of analytical methods applied to physical or engineering problems. Rather, the book covers the abstract analysis that provides the rigorous basis for such applied techniques as function approximation, calculus of variations, PDEs, and Fourier analysis. That's the stated goal of the book, and it achieves it relatively well. My main complaints are the following. First, the previously mentioned deficiency in applied examples. Second, the notation is occasionally not precise or is not clearly explained or is nonstandard. This occurs infrequently and rarely poses a serious problem. The discussion of important definitions and theorems can be terse. The strong points of the book are its excellent selection of topics, large number of well-chosen and challenging exercises, and the concise proofs given for most theorems.The verdict: if you are an applied mathematician or work in the physical sciences, you should consider this book if you want a solid basis in real and functional analysis. ... Read more

Book Description

The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians.Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.

The classic FEM text, written by the subject's leading authors
Enhancements include more worked examples and exercises, plus a companion website with a solutions manual and downloadable algorithms
With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems

Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems.It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations.

Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.

* The classic introduction to the finite element method, by two of the subject's leading authors
* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text
* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms ... Read more

Reviews (5)

An all time classic
From the masters of the finite element method, this may well be the best book ever written on the subject. In this book, the authors come across as the sages of ancient India preaching what they know is the best, guiding us, and setting a stage of research for the years to come. This is a monumental piece of work in the history of engineering.

The milestone in FE analysis
This book is really THE milestone, the only one I really enjoy. A page-turner, a must for all people into FE stuff.

Excellent book for starters in the field
This is the ideal book for beginners in finite elements, though the approach is slightly more theoretical. If you have a good background in linear algebra and are comfortable with matrices etc, you should have notrouble finishing this one. You can aim at the definitive work by ProfessorBathe after finishing this one.

Zienkiewicz and Taylor: Professors of the Century
The enormous influence Zienkiewicz and Taylor have had on the profession of engineering as mentors, teachers, engineers, and researchers, places them among the very best professors this century has seen. May I take thisopportunity at Amazon.com to pay tribute to such professors worldwide forthe spirit they infuse, dynamism they create, and the legacy of selflessservice and excellence they leave behind. Students of 21st century will begrateful that Zienkiewicz and Taylor went before them.

The finite element method bible
There is no more complete review of the finite element method.Furthermore, all notation is written in matrix from without any hard to read diadics.Every section gives explicitly, the implementation of the procedure discussed so there's no guess work required. ... Read more

Book Description

This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory.The new edition contains additional material on the qualitative behavior of solutions of ordinary differential equations, some further details on Lp and Sobolev functions, partitions of unity and a brief introduction to abstract measure theory. ... Read more

Book Description

The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. ... Read more

Book Description

Now available in paperback, this radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Although aimed at the complete beginner, professional mathematicians and physicists will also enjoy the fresh insights afforded by this unusual approach. ... Read more

Reviews (22)

A fresh and insightful perspective on a beautiful subject
Needham's book is a masterpiece which will be appreciated by anyone who already has gained (or is simultaneously gaining) a firm knowledge of the traditional, i.e. more algebraic, approach to complex analysis. In addition to reading it for pleasure, I have used the book extensively in teaching 18.04 Complex Variables with Applications at MIT, not as a required textbook, but rather as inspiration for lectures and homework problems. The book helps me give the students (mostly undergraduates in applied mathematics, science, and engineering) the geometrical insights needed for a deeper understanding of the subject, beyond what is found in various standard texts, such as Churchill and Brown or Saff and Snider (the required textbook for 18.04). As a prelude or companion to Needham's book, however, I would recommend reading one of these other books and working through more straightforward examples of algebra and calculus with complex functions. With that said, Needham's book is a perfect supplement to a first course in complex analysis.

Needham's book is unique in its clear explanation of how the rich properties of analytic functions all follow from the "ampli-twist" concept of complex differentiation. In my class, I use this crucial, geometrical idea from the first mention of the derivative, where it goes hand in hand with the concept of conformal mapping (which is often at the back of introductory texts, but which I think should appear near the beginning). Perhaps the most delighful section of Needham's book is the one where he uses the same ampli-twist concept to give a very intuitive, unified proof of Cauchy's theorem, Morera's theorem, and the fact that a loop integral of the conjugate gives 2i times the area enclosed. The book also contains many clever and challenging problems, which are appropriate to give students to help them "think outside the box", as it were.

The most amazing thing about Needham's book is that it is sure to delight and edify both beginners and experts alike with its simple, geometrical explanations. This is all the more impressive because geometry in mathematics education is more traditionally a vehicle to teach rigorous proofs rather than intuitive understanding.

A Tremendously Insightful Presentation of Complex Analysis
Although mathematical visualization has not been as implicitly forbidden in modern mathematics as claimed by Needham, his work is nonetheless highly innovative even besides his wonderful graphs. The reason is that his prose accompanies very well his extraordinary insight and intuition for the subject. It is purposely not extremely rigorous in order to make the presentation smoother. (This is not so bad as many think. Complex analysis is the target of many excellent books which, fortunately, do not all take the same approach. For more rigor see Ahlfors' "Complex Analysis.")

This book can therefore be an ideal way to get started with complex analysis or even to further one's understanding in the subject. If you are looking for a very affordable predecessor with a similar intuitive style, check Flanigan's "Complex Variables."

Lots of material, great pictures but too chatty
I purchased this book as a reference and because of it's coverage on Mobius Transformations, which is great! My qualms are with the other parts of the book, however. I'll reach for this book or Churchill and Brown when I'm dealing with complex numbers. Browns is much more direct and to the point. There are times that I'll have to flip through several pages jsut to get to the point. Needham often includes a history of the topic and several applications before getting to the mathematics of it. I like reading about applications at the end of the chapters and histories as footnotes (or both in a completely seperate part of the book, i.e. the appendix). If you buy this book, you'll get a lot of great mathematics and wonderful visualizations, but expect a lot of reading that may not be immidiately necessary to your studies.

A marvel, eye-popping, fun. More than five stars!
What a great book this is!

This is a book that any math afficionado must have, and will undoubtedly savor. I frankly don't understand those reviewers who have given this book fewer than five stars. In fact, five stars wouldn't seem to be enough here. This book is among the best math books one will ever find! What else would one want from a such book? It is exciting, friendly, creative, often funny, crystal clear, fresh, deep, and unfailingly courteous to the reader--a quality not always found in math texts.

Additionally, this book succeeds on another level -- it is just plain beautiful. Math, to be great, must be beautiful, while books about great math too often are not. This book is truly beautiful, even artful. The author has taken great care to create beauty here.

I intially bought this book, because as an ex-mathematician whose analysis skills were getting rusty I wanted to revisit complex analysis. This book certainly succeeded in brushing up those old skills, but it also deepened them. The book has marvelous insights and geometric drawings that demonstrate in a clever way the links between complex analysis and other branches of math and physics. How could one not love the lovely and intricate drawings that depict, say, loxodromic transformations on a sphere, or the eye-popping diagrams of rotations in hyperbolic space? They're fabulous! Even the problem sets are delightful.

As a side note, some of the historical glosses about mathematicians are also very lively, and are another source of pleasure here.

On the dust jacket is the blurb--"If you must buy only one math book this year, this is the one to buy." I have to agree. I bought a couple dozen math books last year, and this one outshines the rest. I can't recommend it highly enough, even if you already feel comfortable with complex analysis.

I encourage my fellow readers to pick this up, and see how beautiful a math book can be.

Decent Book for Graduate work but not good main text
I used this book in an introductory Complex Variables course in a top 20 ranked US college. I enjoyed the authors clear explaination of material and clearly british sense of humor. Unfortunately I felt it lacked a great deal of rigor. Proofs were often either just sketched or pictorally shown. I understand that it was the author's objective to give a purely goemetric approach, but I felt that more detail was needed. When I needed to use ideas such as residue classes and other important complex variable conecepts in later math courses, my background was weak.

I agree that the book does have merits. It takes the field of complex variables and looks at it in another way. I do feel though, that a more traditional book would be better to first secure undersatanding of the material. If a student were to continue to graduate work or want to learn more about complex variables, this would be a good supplement. I do not feel though, that this book is a good main, first text. ... Read more

Book Description

This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.

It is currently the only book on the subject with exercises and a large number of examples. ... Read more

Reviews (1)

readable and engaging, good introduction to subject
Krantz has a very readable style and this is one math book that is fun reading (assuming you have the background listed above).No definition causes you to wonder why it was defined, and no theorem causes you towonder why it was proved.

It's also one of the few books that definessheaf cohomology in terms of actual geometric intuition and concreteexamples.Even readers not interested in several complex variables shouldbenefit from the way he treats tangential subjects in this book. ... Read more

Book Description

This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters. ... Read more

Book Description

From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2 ... Read more

Book Description

This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms.This text differs from many other fourier transform books in its emphasis on applications.Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms.The pedagogy in this classic text is excellent.The author has included such tools as the pictorial dictionary of transforms and bibliographic references.In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions.To aid students further, discussions of many of the problems can be found at the end of the book. ... Read more

Reviews (8)

The best book for Fourier transform
When I came to the field of Fourier transform, the book provides me a clear, easy-understanding picture to the field so that I believe any of you can get into the field by use of the book. If you are looking for your first book to Fourier transform, don't waste your time, it is. Even through my life in the research, I depended on it most of the time. It's too great.

Good book on practical, fourier analysis, excellent problems
This book is an old classic in fourier analysis - it emphasizes intuitive understanding and uses images a lot to convey information, e.g. the book includes a pictorial dictionary of fourier transforms, and recommends using the method of dragging a strip of paper to get a better understanding of convolutions. The problems are challenging and very interesting, e.g. one problem asks the reader to explain the differences in spectra when reconstructing a signal by linear interpolation vs. sketching a smooth graph between the sample points by hand. (there are also easier problems for to begin with, before one tackles "engineering" questions as the one above) Highly recommended!

excellent on fundamentals
If you are looking for thorough explanations with great physical insight - this is the book to get. It is for people who want to know WHY more than HOW. However, If you are looking for how (to implement), I suggest the book "Fast Fourier Transform" by Brigham

unusual and rare symbolism to be an engineering book!!!!!!!!
Too confusing...it does not use standard engineering symbols, like for tables, you just need a week to get use to it. For starters...I don't recommend it.

this is not worth buying.... even at a 90% sale.
this is a sad excuse of a text book. It may serve as a reasonable reference.. but as a teaching tool it utterly fails its purpose. the wording are about as clear as sewer water and the problem set are uninformative and tedious for the most part. ... Read more