Product Description
This straightforward course based on the idea of a limit is intended for students who have acquired a working knowledge of the calculus and are ready for a more systematic treatment which also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter. A large number of examples is included, with hints for the solution of many of them. ... Read more

Customer Reviews (2)

Good
Good book.Lacking in certain important mathematical concepts like lim sup and lim inf, but otherwise good so far.

A good little "bridge" from School Maths into University
It is amazing that, despite the changing fads in the curriculum, this book has the quality to remain a steadfast bridge from School Mathematics on the first steps into the realm of the Maths specialist for over 40 years now.

The recipe is simple: keep it short, keep it sweet, keep it simple! Mr Burkill has produced a fine little book that gently guides the new student embarking on a specialism in Maths. The author has struck a good balance between the problem solving so familiar at school and introducing the rigour of Mathematical Analysis.

Familiar concepts like differentiation and integration are brought into play right after a quick refresher on numbers and then introducing the notion of limit within the framework of sequences. The delta-epsilon construct is used to great effect to give meaning to the ideas of convergence of sequences and the continuity of functions.

These then lead naturally to the Differential calculus where previously learnt ideas like the rules of differentiation are placed in a rigorous setting and interesting elementary analytical results such as the Mean Value Theorem and Taylor's theorem are discussed. The chapter on Infinite series together with the elementary rules for testing for convergence is followed by a chapter on the special functions of analysis as defined in terms of series - e.g. exp, log, sin, cos, etc.

The chapter on the Integral Calculus makes a natural next step utilising the ideas of an integral as a limit and of infinite series. Specific techniques such as the integral to infinity and approximation methods are placed on a rigorous footing. The final chapter introduces functions of several variables.

The book has lots of worked examples within the text, which aid understanding of new material. As a bonus, there are also several end of section with notes/hints at the end of the book.

Overall, this is a gentle introduction to Analysis and will help anyone who is overawed by the subject on first encounter. ... Read more

Product Description
A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool.

The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' ``fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. Also added is adiscussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions. Since the L² techniques are essential in the proof and plurisubharmonic functions play such an important role in this book, it seems natural to discuss their main singularities.

... Read more

Customer Reviews (3)

excellent if you understand it
zooom.....Here's a clue;As I recall, he does all of one variable complex analysis in an introductory chapter less than 20 pages long, including a version of Cauchy's theorem more general than I wager most have ever seen.

Book by a communication-challenged but expert mathematician
This book is pretty hard to read.
It's extremely terse, for one thing.In one place he said something followed from the Hahn-Banach theorem.It didn't _look_ related to the HB theorem.So I find a corollary to the HB theorem which does look related.But it requires the Riesz representation theorem to work.So I read the proof of the RR theorem for positive measures.That also doesn't quite do it.I puzzle a bit, then find there's a RR theorem for complex measures.And, Finally this one sly little sentence makes sense!
If you care about understanding the math, making sense of it, it is sure going to be slow reading!
But, a lot of it is also fairly straightforward.
It has a few typos, but for the most part it's carefully proofread.Typos are especially frustrating when his writing is so compressed, because there isn't much of a context to make sense of them.
He uses new symbols without defining them.You have to guess what they mean.For example, if V is an open set, C^k(V) means complex valued functions on V that are k times continuously differentiable.He does define that.Then he starts talking about C^k(K), where K is the closure of an open set, without saying what he means by being differentiable on the boundary.Maybe he only talks about C^k(K) if the boundary of K is nice enough that you can define a derivative on it?Then he mentions C^k_(0,1)(K).Leaving you to figure out from the context that he means differential forms of type (0,1) with coefficients in C^k(K).Later, he talks about a "schlicht domain" without defining schlicht.
He uses idiosyncratic notation, so it would be hard to use the book as a reference.You'd have to figure out what all the symbols mean, and he doesn't list them all in his symbol table at the start of the book.
But, I also felt I was hearing from a truly expert mathematician.I wasn't surprised when I found out he got a Fields medal.
It has been awfully frustrating reading about multivariable complex analysis, because a lot of the authors do make mistakes.Gunning and Rossi's book had a lot of mistakes.Robert Gunning's later book, "Introduction to holomorphic functions of several variables" also has many mistakes in proofs.The mistakes in Gunning and Rossi had been fixed up, but Bochner's tube theorem, which is new in the later book, had a wrong proof.An article by Sin Hitotumatu purported to prove the theorem, but there was a big gap in the proof!But Hormander, though it took me ages to puzzle through his writing, actually did prove the tube theorem.There were no mistakes in Hormander's book as far as I read it.Being right, not using up your time with long proofs that have mistakes in them, makes up for a great deal of obscurity.And reading his proofs can be a delight like watching the clever conjurations of a wizard.
I've only read the first 42 pages of Hormander's book.But I imagine these attributes I describe only get more intense once he's past the introductory things.
Later books on multivariable complex analysis have been written for people who have trouble with compressed mathematical gems like Hormander's book.
His book is referred to a lot by other books, although probably hardly anybody actually tries to follow his reasoning.
Laura

High-level math, as expected from Hormander
I started to learn several complex variables a few weeks ago, and I noticed the absolute lack of textbooks on the subject. Probably the book that comes more naturally as an extension of undergraduate complex analysisis Gunning and Rossi, but this title is out-of-print (even finding a usedcopy is nearly impossible. Believe me, I've tried hard).

So, we haveHormander's book. Lars Hormander is known for writing high-level math texts(both in quality and difficulty), as seen in his famous 4-volume seriesabout PDE's, and this book is no exception. His point of view is morerelated to his area of research (PDE's, again), and his demands forprerequisites are higher than GR (basics from Lebesgue integration,differential forms, algebra and point-set topology are more than welcome),but this book is a masterpiece of mathematical craftsmanship. The methodshere developed are often unique, and the author presents the subject in afully rigorous way. Along with the fact that it is one of the very fewbooks on several complex variables still in print, this is a very valuabletext, set in a high standard of excellence. My only complaint is theobscenely high price for a book so important. Several complex variables arean indispensable background for complex manifolds and algebraic geometry,and several important topics in theoretical physics (string theory, twistortheory, conformal field theory), and it's a shame that books like GR goout-of-print without any others for substituting them. Hormander's bookdoesn't go much deep in these directions, but you won't find any other bookin print on the subject with such a high quality. ... Read more

Product Description

This monograph presents a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst. It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied.

Customer Reviews (1)

An excellent treatment of mathematical methods for economist
The monograph covers advanced mathematical methods for economists. Itincludes chapters on general topology, topological vector spaces, Rieszspaces and Banach lattices, measure and integration, etc. While the bookdoes not contain (hardly) any economics, the mathematics coveredisselected under the aspect of later applications to economics. The bookcontains for example a long chapter on correspondences, a topic which ishardly covered by any standard math book. The presentation of themathematics is throughout clear and precise. The advantage of the book isthat it covers a wide range of mathematical topics, which could not befound together in a book before. Graduate students in economic theory canuse it as a text book, but it can also be used as a reference book. Theonly lacks of the book are that there are no exercises and that not allmath areas important to economics (e.g. differential topology) are covered.Overall, this is an excellent book and should become part of the library ofeverybody interestedin mathematical economics. ... Read more

Product Description
Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autónoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, $H^1$, $BMO$ spaces, and the $T1$ theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between $H^1$, $BMO$, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the $T1$ theorem, which has been of crucial importance in the field. This volume has been updated and translated from the Spanish edition that was published in 1995. Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis. ... Read more

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The Colloquium series bestseller. ... Read more

Product Description
This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrandemphasize the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. ... Read more

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Customer Reviews (19)

An okay introduction
This book is pretty clear for the most part.The authors present the material in a way that tempts readers to skip the proofs at the end of each chapter.For that, this book loses a star.

Dense but clear and concise
It takes a while to get through the explanations of the general topics, but they provide excellent examples in each section of the topics being discussed. The answers in the back of the book, however, are pretty bare boned and not entirely that useful for understanding what you did wrong.

Good book - lot's of mistakes
Most people taking a course like this use Rudin and this is a reasonable supplement but there is a good bit of errata that should be downloaded from the author's site.Pugh's "Real Mathematical Analysis" is an alternative.

Lovedit as a student and as a professor
This was my favorite book as an undergraduate student and I've taught from it as a professor.It is an excellent geometric approach to analysis.It can even help students who have difficulty with epsilon delta proofs understand the geometric intuition behind them.The construction of the real line at the beginning is daunting for students who aren't clear about set theory and sequences already but a few supplementary materials can help the students out there (see my webpage notes on real analysis for example).The proofs are hidden which makes it a challenge for students to try prove everything themsleves before peeking at them, but they are available.Just remember to tell your students where they are!

As a student I loved the book because it allowed me to learn everything on the metric space level while allowing students who prefer to stay in Euclidean space to do that.Now I am a metric geometer.

very helpful book
I am using this book to teach myself analysis. Because my mathematical background is limited, I cannot assess what the book is missing, or whether alternative methods of presentation would be more insightful. But in terms of clarity and comprehensibility, the book does very well. The authors write very carefully and are not cryptic; the proofs and examples are well-presented, and I rarely feel lost. The book is rigorous but not, let's say, snobbish. I am learning a lot from it. ... Read more

Product Description
This book an EXACT reproduction of the original book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Customer Reviews (1)

Just a sequence of random code
I downloaded a sample of this book on my Kindle for PC. It is really awful. I just saw a sequence of random. No math nor readable text. If I didn't see a picture in the middle of page, I wouldn't know this was a sample book!! ... Read more

Product Description
/*4579F-0, 0-13-045796-5, Kosmala, Witold J., Advanced Calculus: A Friendly Approach, 2/E*/ This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting. Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration. For individuals seeking math fun at a higher level. ... Read more

Customer Reviews (5)

A big mistake
I selected this text for my undergraduate analysis class. It was a big mistake
it starts out nice and chatty and "friendly" but the author soon buries the
material in detailed tangential remarks. Particularly annoying is
his comparing exercises to many previous ( and future!!) problems in
the text. Togetherbwith the remarks the text grinds to a halt trying
to leaf back and forth to reference them. My students found this book
to be very difficult. Even simple things to prove he sometimes refers
the reader to previous material.My students need help on simple
things involving series say. He includes so many different ratio tests
for example and then has few straightforward probs for them to do.
It was an ordeal selecting problemsfor them to do.
Many of the easy ones he refers them to previous probs in
the text so the student refers back to the earlier solution instead
of proving it himself. A really bad experience!

This is a good book...but
The idea of this book is great - you are sitting in front of Rudin, you have no idea what to do and all of a sudden you open this book and things become clear!Umm, not quite.First, this book has had problems with a multitude of typos (see the author's web site).Second, the title is stupid.There is no such thing as a 'friendly introduction to analysis'.That's an oxymoron if ever there was one.This book is very good at explaining basic ideas and giving you some insights BUT IT STILL AIN'T RUDIN (and its discussion/proofs of convergence tests is weak since they all link back to geometric sums and that is not mentioned here).If you want to study analysis you eventually have to make large pot of coffee, put butt in chair, take out pencil and a raft of paper and start working - without tv, ipod, music, dog, wife, etc.Will this book help some?Sure, it is a nice reference.Will it teach you enough to say you know analysis.No.

A suffocating read.
Bunch of lies the two reviewers gave. I bought the book, tried to learn from it, and ended up hating the book. I realized pretty fast that the book is like any ordinary real analysis book: routine restated theorems, routine common simple problems, routine impossibly hard exercises, and routinely almost zero help from the back of the book. Sure, sure...I needed help from this book for a class using a different book while that book is presented exactly the same way as this book. I know for sure that this book or any book on real analysis anywhere is set out to doom my head to never ending death of my desire in mathematics. Can't anybody publish a book called "Real Analysis for Dummies"? Cause I surely need to buy that book.

Having problems with analysis? GET THIS BOOK!
This is a wonderful book for all of you out there that are struggling with analysis because your professor has chosen a traditional analysis text that is very terse like Rudin. The problem with so many of the traditional analysis textbooks is that you need a professor by your side guiding you, and without that type of help a student beginning analysis would be completley lost.

So to remedy that situation I strongly recommend all of you future analysis students to first take a look at this book.I think one of the main problems with students taking analysis is that it overwhelms them at first because it is nothing like the rest of the undergraduate curriculum in school.The math programs at most universities ignore analysis until the senior year.Typically before that students are in math courses that are purely computational. Usually learning calculus out of Stewart or something and never really touching on the theoretical aspects of calculus.

So of course when a student hits analysis its going to be mind boggling.That is why this book is so wonderful. It is sort of bridge from computational calculus to advanced calculus.It is not intimidating like so many of the analysis books. It approaches each subject matter in a very clear fashion. It has many examples which is rare for an analysis book.

I found chapter 8 to be a wonderful treatment of sequences and series of functions.I think many students would agree that concepts such as uniform convergence can be confusing but the author does a great job illustrating this somewhat complex topic.

All I can say is I wish when I was taking analysis I had access to this book. I think this book is great for an undergraduate analysis class as well as a first year graduate level class.
I think also if you are doing self study to prepare for examinations I think this is a great reference book.I really appreciate the author's efforts to write an analysis textbook that is so easy to read.

Great book for learning, reference, and review.
The appeal this text has to readers is that it is approachable, readable, and thorough. Among the topics included are proof techniques, sequences, limits, and single and multi variable calculus.

In comparison to other books I have studied concerning this material, this text has been written with students making the transition from computational mathematics (calculus sequence, linear, DEs) to analytical, theorem proving mathematics in mind. There is a strong emphasis on conceptual understanding and on how the topics are related to one another, with motivation provided for the study of each topic. Theorems are presented in a logical sequence, a large number are proved, and the discussions are very useful in pointing out important aspects of theorems and special cases to consider.

Concerning exercises, one nice thing I have come to appreciate is that, while being an analysis text, computational exercises are provided to ensure that the concepts are fully understood. Following these exercises, the numerous examples will help when completing the requested proofs.

The second edition is noticeably slimmer than the first. This is mainly due to a change in typesetting (which is better, in my opinion; the text is closer together so the pages look more full). There was one chapter removed on Fourier Series, but this can now be downloaded from Dr. Kosmala's web site. Aside from this one removal, there is more material presented in the second edition to go along with the corrections and rearrangements to the first.

Analysis can be a difficult subject to grasp, so I highly recommend this text for (as the preface says) its "clarity, readability, and friendliness." ... Read more

Product Description
Significantly revised and expanded, this new Second Edition provides readers at all levels---from beginning students to practicing analysts---with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas.

Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing.

This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes:

Features:

a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more

extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities

new material on Measure and Integration

many new exercises

and much more ...

The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straight-forward volume that readers---from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods---will find useful both as a reference and as a guide to real problem solving.

About the authors: Elliott Lieb is Professor of Mathematics and Physics at Princeton University and is a member of the US, Austrian, and Danish Academies of Science. He is also the recipient of several prizes including the 1988 AMS/SIAM Birkhoff Prize. Michael Loss is Professor of Mathematics at the Georgia Institute of Technology. ... Read more

Customer Reviews (3)

A tremendous jumpstart into modern mathematical physics
I am a physicist with a somewhat limited mathematical background. However, I decided to 'break in' in modern mathematical physics, and that meant acquiring first a modicum of functional analysis and the required measure theory, harmonic analysis, and operator theory that goes with it. If you can afford the time, the classical learning path through, e.g., Kolmogorov & Fomin > Rudin (R&C) > Reed & Simon I (a path that I recommend, by the way), with possible excursions into ODEs and PDEs, probability theory, and modern geometry, is the safe way to go. If you cannot afford the time, read Lieb & Loss. It provides a tremendous jump start into what really matters for a beginning mathematical physicist: a little measure theory, L^p spaces, Sobolev spaces, a bit of Fourier analysis and PDEs, and inequalities -- lots of them (integral, Sobolev, variational). The main theorems are stated, most with proofs, and put into use.

I had a mathematical physics teacher in graduate school that once said (somewhat half-jokingly) that all you need to know is the monotone and dominated convergence theorems, the Fubini theorem, the Borel-Cantelli lemma, the Euler-Lagrange equations and how to resolve the identity using plane waves. This book by Lieb & Loss is a testimony to his confession.

A start in analysis.
A start in analysis.-- For some number of years, Rudin's "Real and Complex", and a few other analysis books, served as the canonical choice for the book to use, and to teach from, in a first year grad analysis course. Lieb-Loss offers a refreshing alternative: It begins with a down-to-earth intro to measure theory, L^p and all that...It aims at a wide range of essential applications, such as the Fourier transform, and series, inequalities, distributions, and Sobolev spaces,--- PDE, potential theory, calculus of variations, and math physics (Schrodinger's equation, the hydrogen atom, Thomas-Fermi theory... to mention a few.) The book should work equallly well in a one, or in a two semester course. The first half of the book covers the basics, and the rest will be great for students to have, regardless of whether or not it gets to be included in a course. This choice of book is also especially agreeable to grad students in physics who need to read up on the tools of analysis.

An excellent course of analysis with a theme
By the end of the sixties Dyson and Lennard, for the first time, proved that matter is stable. More precisely, they proved the thermodynamic stability of Coulomb matter. This was a landmark of mathematical physics, and a huge one: a very long and hard paper. A few years later, Elliott Lieb and Walter Thirring substantially improved the great Dyson result, dramatically cutting its length while improving important estimates. A very good review of these results can be find in the volume 4 of Thirring's "A Course in Mathematical Physics". Even the book version is a bit hard to read, as much mathematical analysis is required. The "Analysis" of Lieb and Loss is a book on analysis which has as a theme the great result of Lieb and Thirring. It is a real book on analysis. The chapters are named "Measure and Integration", "Lp-spaces","The Fourier transform", "Distributions", but also "Potential Theory and Coulomb En! ergies" and "Introduction to the Calculus of Variations", where nothing less than the Thomas-Fermi atom is rigorously studied. In order to leave no doubt that hard analysis is present, there are two chapters on Inequalities. After studying this splendid text the reader will be a better analist and, if he cares to, can start reading the proof of stability of matter. The proof of the pudding is NOT in the eating! ... Read more

Product Description
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.

With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.

Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory. ... Read more

Customer Reviews (9)

Nice choice of topics
If possible, I would give this book 4.5 starts, just because I don't think it is quite as good as the great classic by Conway, "Functions of One Complex Variable" (which treats all the standard topics).On the other hand, Stein and Shakarchi's book is beautiful, lucid, and obviously written by one of the grandmaster analysts of our time.Also, I give it five stars for including a beautiful treatment of the Paley-Wiener theorem, a topic that doesn't usually make its way into elementary complex analysis texts.Finally, this book has the best treatment I've seen of the Hadamard factorization theorem.

Good
Exactly same item as I expected.
This book is a little hard for undergrad student.
There is no solution for exercise question.

Informative, but too dense
The text packs a lot of information very tightly, making it difficult and slow to read. As a textbook or reference material, it works fine, but expect to do most of your learning in class rather than by reading the book.

it is just good
I got a copy of this book. It is a text for undergraduate students in pure mathematics.It is a good reference for elementary proofs of most common theorems in complex variables. However, some important theorems (ej: Three lines lemma and Picard theorem) are placed as exercises and problems. It is not a book for applications in engineering, its applications are taken from number theory.At some places it refers to sections or chapters in other books in the Princeton lectures in analysis. I think this is a four starts book.

The exercises are not very good
I used this book in a first year graduate course.I found the exposition not very clear, and the exercises particularly uninteresting.If you have the choice, I definitely recommend Gamelin's Complex Analysis instead. ... Read more

Customer Reviews (1)

Ray M. Bowen
At first, I found this book to be difficult reading. However, after a very serious attempt to discover the Author's intent, I truely began to cheerish the information presented in this book. One day I plan to contact Mr.Bowen, and maybe study with him for a time. ... Read more

Product Description
Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research. Written for an interdisciplinary audience of engineers, applied mathematicians, and other scientists with little or no knowledge of wavelets, readers with an undergraduate background in applied mathematics or engineering will appreciate this book. ... Read more

Product Description

This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.

From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY

Customer Reviews (5)

Abeauty
I learned this material years ago but when I need to
look things up, this book has everything, well written.
For example the Taylor expansion with multinomial notation
is given here. The writer treats the undergraduate student's
intellect with respect. This is a serious book.

Just like every other Lang text
This book typifies Lang's style. If you enjoyed any of his other books you'll enjoy this too. Like seemingly all of his texts, it has a section on the inverse function theorem and makes quite a deal out of it. Overall, it is quite comprehensive, but there's little motivation for the proofs so things can be a bit boring. Both Rudin and Browder cover the same amout of material in far fewer pages, and they have better excerises too.

Solid, complete reference to basic analysis topics
Serge Lang's "Undergraduate Analysis" offers an impeccable selection of topics and exercises for the student wishing to broaden his/her knowledge of analysis. The proofs of theorems can be terse at times, but a hardworking student will gain much through a thorough reading of the text. Also, Lang concentrates many of his exercises on estimates, which is an art form that is slowly dying among undergraduates (and graduate students as well, sad to say). Many of his problems require only the triangle inequality (the basic tool of estimation) and ingenuity (and hard work) from the student. I would strongly recommend this text for anyone who wishes to fully understand and appreciate the results and techniques of basic real analysis.

okay
I personally don't care much for this book.It's too terse, and there are nowhere near enough examples.I have about 6 analysis books and this is the one I look in the least.It seems to cover a lot of stuff, but maybe too much-- it wouldve been better to focus more on some more elementary topics.For instance, he spends about one and a half pages introducing the derivative.So if you want a book that glosses over more elementary concepts and leans heavily toward a graduate level, this book's for you.At my school we were supposed to learn advanced calculus from this and it is not good for that at all.For advanced calc try robert stritchart's Way of Analysis (the best book on analysis I've ever read) and for analysis Intro to real analysis by kolmogrov (only 10 bucks or so and actually better than most books costing a 100)

Great intro to real analysis with logical format
Lang's book is an excellent introduction to real analysis that tries to build the reader's knowledge from the ground up.Lang starts with fundamental ideas from calculus and then proceeds in a logical way.Havingtaken Lang's course, for which this book was designed, it is clear to methat this book is a result of Lang's many years of experience teachingundergrads.I highly recommend this book to anyone who wants a solidfoundation in analysis. ... Read more

Product Description
Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting. ... Read more

Customer Reviews (2)

Five stars for content; two stars for printing
I'm a math professor in the middle of developing an introductory functional analysis course whose prerequisites will be elementary linear algebra and metric space theory and whose intended focus will be on the *abstract* theory of normed spaces and bounded linear operators between them.This book by Bollobas is about the best fit for the class that I've been able to find after an extensive search.The author covers about the right topics in about right the depth, and from what I've been able to tell it is well-organized and well-written.

During the development of this curriculum, I've been using a 1999 printing of this book borrowed from the library, and it impressed me enough that I ordered a copy of my own from Amazon, which arrived just this afternoon.To my dismay, I learned that this book, like so many of Cambridge University Press's older works, has fallen victim to the "digital printing" scourge.Contrary to what Amazon's "Search Inside!" feature indicates, the copyright page now reads "Transferred to digital printing 2004".Not that you need the copyright page to tell you that, because the loss of crispness in the typography makes that abundantly clear.And, of course, this new copy has a "perfect binding" (a misnomer if ever there was one).If you like a book with a nice professional look to it, don't get your hopes up with this one.What a shame.

Good writing, OK coverage
This undergrad text is very clear and Bollobas has a friendly style of writing. The coverage, though, is rather narrow and there are no applications. So I like Kreyszig better. ... Read more

Product Description
This volume contains all the exercises, and their solutions, for Serge Lang's fourth edition of "Complex Analysis," ISBN0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at the undergraduate level and cover the following topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in Chapters 9-16 is more advanced. The reader will find problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. ... Read more

Customer Reviews (3)

I have little taste for answer books, especially when they are wrong
I gave a take home test of problems from Lang, because the answers are not in the back of the book.A student challenged my answer to one question, because Shakarchi says the answer is something different.I did not realize anyone had gone to the absurd trouble of publishing answers to the excellent exercises in Lang's book until then.But Shakarchi is wrong, having made a careless error.Reading books of answers to problems is like reading a book about physical exercise only worse, since not only do you not benefit from the exercise of doing it yourself, but you lose most of the potential benefit of the exercise after seeing the answer.At least with physical exercise you do not lose anything from watching it done if afterwards you do it yourself.Look on page 85 of this book where Shakarchi asserts that problems VI.1.26b and VI.1.26e have the same answer because the denominators have the same residues,Well how about the numerators?In 26e the z in the numerator implies that the terms of the laurent series of the quotient are not all of even degree anymore, so I claim (check it!I could be wrong too)the correct answer is that all residues in that case are equal to 2, not zero.(This comes from 2= 1/(1/2) the quotient of the coefficient 1 of the z in the top, and the first non zero coefficient 1/2 ofthe taylor series of 1-sin at /2.)So without having read any more of this book, even if this is the only error,I say it is almost worthless to someone really wanting to learn the subject.But if you are like someone who cannot exercise without watching a Jane Fonda video, and you do buy this book, please work the problems yourself, and do not just take the author's word for them.I do recommend Lang's book, and the exercises. Probably my favorite complex book is that by Henri Cartan available in a cheap paperback, and the one by Frederick Greenleaf (available used and in libraries) is excellent for beginners, and he gives the answers (but not the solutions) to most of his exercises right in the book if you want that.

INCOMPLETE EXPLANATIONS
This book cannot be used without purchasing the actual book which it represents. This book has some solutions for another complex analysis book. What I thought was, that this book is similar to something like Schaum's solved problems (which is independent and not dependent on another book). In many cases, there is no work shown at all, and simply the answers. So its really of no use and has a deceptive title. I already had 4 other books in complex analysis, so there was no need for me to purchase another book which it represents.

The Right Stuff !!!!!!!!!!!!!!
I bought this book with the goal to enhance my problem solving skills on complex analysis. I am a theoritical physics student and needed to gain a very comprehensive and operational understanding of the topic. This book had it all: it's very well written, very rigourous and gives an extra dimension to just reading a pure text explaining the theory of the subject. I wish we had this type of books in physics ! Lang's book and Shakarchi's solutions are the winning combination to learn complex analysis!!!!! 2 thumbs up ... Read more

Product Description

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study.

 Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added.

Review of earlier edition:

"...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references."

R. Glowinski, SIAM Review, 2003

Customer Reviews (1)

About Theoretical Numerical Analysis <br />by Kendall E. Atkinson
The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations.

If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".

The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods. ... Read more

Product Description
Outstanding text treats numerical analysis with mathematical rigor, but relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency. Problems—some strictly mathematical, others requiring a computer—appear at the end of each chapter.
... Read more

Customer Reviews (5)

5 Stars for undergrads
If you are looking in to 3d Nurbs buy this book. If you are looking to build a robot from scratch buy this book. It may mean taking calculus and linear algebra but the algorithms are very advanced and quick. This is the math that every corporation would like you to have if you are an engineer. Plus it helps you understand many of the mathematicians. After reading this book you have excellent under pinning for your name.

P.S. This may be good for white hatter as well but I don't know since I am not into cryptography.

P.P.S. Did you always think that Sin() was a magical function? Well you will learn more than you every thought possible with this book. The optimization on you code can go through the roof. Plus this seems to be (but I still have not confirmed) a good way of understanding O notation and not to mention NP complete algorithms (Such what classifies a NP Complete problem).

Archaic First Course in Numerical Analysis
A constant in numerical analysis for years the second edition has not kept pace with the way mathematics is contemporarily taught to engineers and scientists.The book appears to assume an older format of learning mathematics was used by the reader. The reader will soon be seeking additional texts to make this one understandable.

A classic and a bargain at that
I lost my original copy during my last move. Therefore, I was overjoyed that an inexpensive paperback version had been printed. A must for the numerical analyst's library.

good intermediate text on numerical analysis
This is a good intermediate text on numerical analysis. The development of the underlying real variable theory is much more rigorous than the closely related and more recent text "Numerical Recipes in C". Also, there is more attention paid to function theoretic considerations such as notions of continuity and compactness. This is basically an introductory numerical functional analysis textbook. There are numerous good examples sprinkled throughout the text. To get the most out of this book, you need a working knowledge of advanced calculus, real analysis and linear algebra.

Simply the best you can get (at this price)
This is the republication of the 2nd edition published by McGraw-Hill, 1978, with minor corrections. This Dover edition also includes 50 pages of Hints and Answers to Problems, which is very helpful. It is one of the 14 reference books listed in the Numerical Recipe in C: The Art of Scientific Computing, and the authors of the Recipe book says, of the 14 books, "These are the books that we like to have within easy reach." A. Ralston, of SUNY Buffalo, also co-wrote a book, Discrete Algorithmic Mathematics(DAM), which is easy and fun to read. But I am puzzled by the words - "Well-known and highly regarded even by those who have never used it." - on the back cover of the A K Peters edition of DAM. What do they mean? ... Read more

Product Description
In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier s introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy s attempts to establish a firm foundation for calculus, and considers his failures as well ashis successes. It culminates with Dirichlet s proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet s proof. ... Read more

Customer Reviews (3)

Excellent sequel
If you had calculus in high school or college then you learned about Newton, Leibnitz, and Riemann but probably did not encounter Lebesgue (pronounced le-bek). At the University of Alabama Huntsville learning about Lebesgue integration is key to advancing into graduate studies in mathematics. The natural follow-on course after Calculus I and II, etc. is Real Analysis. This book, using Lebesgue integration methods, is a good sequel to Lebesgue calculus.
I purchased this book, after reading about it in the Mathematical Association of America (MAA). For autodidacts like myself, it is a good first introduction to the topic.

A radically false account of history
This is not a bad book, but it does everyone a huge disservice by pretending to be historically informed when in fact it is propagating harmful and stupid myths that have no basis in historical fact whatever. An example should make this clear.

"Daniel Bernoulli suggested in 1753 that the vibrating string might be capable of infinitely many harmonics. The most general initial position should be an infinite sum of the form
(2.71) y(x) = a_1 sin(pi x / l) + a_2 sin(2 pi x / l) + a_3 sin(3 pi x / l) + ...
Euler rejected this possibility. The reason for his rejection is illuminating. The function in equation (2.71) is necessarily periodic with period 2l. Bernoulli's solution cannot handle an initial position that is not a periodic function of x. Euler seems particularly obtuse to the modern mathematician. We only need to describe the initial position between x=0 and x=l. We do not care whether or not the function repeats itself outside this interval. But this misses the point of a basic misunderstanding that was widely shared in the eighteenth century. For Euler and his contemporaries, a function was an expression: a polynomial, a trigonometric function, perhaps one of the more esoteric series arising as a solution of a differential equation. As a function of x, it existed as an organic whole for all values of x. ... To Euler, the shape of a function between 0 and l determined that function everywhere." (p. 53-54)

There is not a single line anywhere in any pre-19th century mathematical work that comes anywhere near making this sort of claim. Self-righteous "mathematicians" have invented these myths to justify their dogmatic and authoritative mode of "teaching" and their passionate hatred of intuition. In falsely lending these propaganda fabrications a veneer of historical truth, Bressoud is perhaps the worst lier of them all. It is not Euler who is "obtuse," but Bressoud. There was no "basic misunderstanding widely shared in the eighteenth century"; rather, the "basic misunderstanding" lies with Bressoud and his fellow poseur historians of today.

All of this is easily established by simply reading Euler. The relevant paper is E213, which is readily available online. Let me summarise what you will find if you read that paper.

First of all, Bernoulli never claimed that (2.71) can express any initial position of the string. He merely argued for a general series solution of the vibrating string equation which *implies* that the initial position is of the form (2.71). Hence Euler's main objection, which is this: I can bring the string into any position whatever, let go, and it will move according to the vibrating string differential equation. Thus Bernoulli's solution is not completely general insofar as (2.71) does not express any possible initial position of the string. And since Bernoulli has provided no argument that (2.71) can in fact express any initial position, nor in fact any method for calculating the coefficients a_i, we have no reason to believe that his solution is completely general. At this point Euler preempts a hypothetical counterargument: perhaps, says Euler, some might argue that "owing to the infinite number of undetermined coefficients," equation (2.71) "is so general as to include all possible curves." This, however, is plainly false, Euler points out by noting the periodicity properties of (2.71). Now, at this point it would be possible for a Bernoullian to retreat still further and say that (2.71) can express any function, not on the real line, but on the interval [0,l]. This is a perfectly valid argument, but it is an argument which Bernoulli never raised and which Euler never claimed to have refuted. So much for the periodicity argument, which Bressoud has obviously distorted most unfairly. But worse still is Bressoud's generalisation from this case to the alleged "basic misunderstanding." This is sheer stupidity and fabrication, as is plain to anyone capable of reading at a fourth grade level. In fact, every last word of it is plainly and unambiguously rejected by Euler in the very article in question when he points out that the initial position of the string can be any curve, which "often cannot be expressed by any equation, be it algebraic or transcendental, and is not even included in any law of continuity."

Getting there naturally
I am a topologist by training who was Shanghaied into being an analyst when I was hired as a teacher.As a consequence of this, the Advanced Calculus course I taught was rather heavy on topology.

Over the course of time--having been transformed into more of an analyst that I would have ever dreamed--I've come to the conclusion that analysis is best learned before topology.

This is a text that accomplishes that by using the historical approach.

One learns how Newton approached problems, how Euler did, how Cauchy did.Not only is it interesting, it is enlightening.I've taught this course for 15 years now, and of all of the approaches I've taken, this has been the most fruitful.

My students have come from calculational courses, and the historical approach of this book provides a bridge over which they may come into the land of proof.They also see the issues that caused the need for modern rigor face to face

I do supplement the course with material that is more modern (Hardy's book A Course of Pure Mathematics) and material on the Riemann integral, but I've been spoiled for any other approach.

... Read more