Product Description

A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.

Product Description
"Complex Variables and Applications, 8E" will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions. The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections. ... Read more

Customer Reviews (38)

quick delivery and good condition
The book was in better condition than stated. It was also a very cheap price. Win win

Lacks any motivation for the material, but is good for computational proficiency
I used this book in my introductory complex variables course, which at my large university was primarily aimed at the physics majors and electrical engineering majors who wanted to know more about computing with complex functions. This is where the book excels, at making you computationally efficient in the complex plane. This includes the ability to solve integrals, find complex roots, understand a few basic theorems, and use them to make useful bounds. The ubiquity of complex numbers in the applied sciences allows people who know more complex variables to have a slight edge over their fellow classmates.

There are many examples in the book to help point out non obvious uses of the results, and also to point out the many pitfalls the less careful student may encounter when studying complex variables for the first time. Also abundant, are the exercises at the end of each chapter. Many of whichhave answers or hints at the back of the book, and many of the problems are more interesting than the lessons themselves which is always a good sign.

I should mention that this book does involve proofs with their associated theorems, and may also serve as a nice introduction into the theoretical side of Calculus (which we call "Analysis"). The proofs are complete, and require little in the way of filling in the blanks yourself. However these proofs are entirely mechanical, which means that they boil down to algebraic manipulation over conceptual/geometric reasoning almost every time. You will be able to work with the theorems, and prove some of them, but most people will have no insight into why it actually works.

Perhaps the absolute worst part about this book, is the almost complete lack of pictures. Complex analysis is a very geometric subject. Almost every algebraic proof could be preceded/replaced with simple reasoning that unveils how the geometry of the subject necessitates the theorem. The beauty of the subject can not be seen without more figures, and more time spent on the intuition behind the ideas. To see how amazing this subject can truly be, I can't recommend strongly enough Tristan Needham's "Visual Complex Analysis". Visual Complex Analysis

Needham's book is a bit slower, and is less computationally focused, but its reasoning is so clear that it makes the multitude of theorems seem obvious and necessary. Every aspect of complex variables from Cauchy's equations, to the exponential function is made intuitive through carefully looking at why such things should be. The multitude of amazing figures are used to incredible effect. After you read Needham's book you'll really appreciate the greatness of the thinkers who preceded the subject, and get a little bit closer to thinking like a real mathematician.

The problem is, you'll never remember all the results and techniques unless you either use them frequently outside of the classroom, or actually took the time to see why the results are true at a level that can be conveyed with words. So unless you need this book for a class I can't recommend paying the steep price. If you can find it at a library it's worth checking out. But if you had to pick one I would go with Needham's book any day, you'll thank me for it later.

Good introduction to Complex variable
Regardless of the price which is little too expensive, it was a good book to start with Complex variables.

Misleading Item
I have no problem with the book. However, what Amazon is not telling you is that this is NOT the original book, but the INTERNATIONAL cheap-paper edition. You can buy the real edition brand new for 20% less elsewhere, and this version for practically nothing. Shame on Amazon.

Very good complement
Very good book to complement Complex Variables and Applications by Brown and Churchill. The solutions are well described and easy to understand. ... Read more

Product Description
This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool. ... Read more

Customer Reviews (1)

A good, if expensive, introduction to functions of a complex variable
Suitable for a one year course in complex analysis, at the advanced undergraduate or graduate level, this is a pretty good introduction to the subject, with well-written, detailed proofs and lots of exercises.If you take the time to work the exercises, you will learn the subject, and you will learn it well, and if you have trouble with some of them, you can look in the back for answers, though if you have this as a textbook, your professor will probably assign problems whose solutions are not in the book.

The chapter on Cauchy's integral theorem is particularly good, describing the material in detail and providing a nice illustration of homotopy of curves.Studied dutifully, this can help a student through one of the thornier areas of the subject, often an area that trips those new to complex analysis.That alone could make the book worth the price.

This is, though, only an introduction, and a student hoping to cover more advanced material is urged to consider William Veech's "A Second Course in Complex Analysis" or some other books suitable for that purpose. ... Read more

Product Description
Noted mathematician offers basic treatment of theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a systematic, though elementary, exposition of theory of abstract complex manifolds of one complex dimension. Topics include power series in one variable, holomorphic functions, Cauchy’s integral, more. Exercises. 1973 edition.
... Read more

Customer Reviews (5)

Horrible
The first time I ordered this book I received the wrong book and then following the instructions on the invoice returned it.Then I reordered and should have received the book by now, but have not!And I need this book for my work!I am thoughly discusted by the extremely poor service I have gotten here and am thinking I should do business with some other book company from now on -- any other book company!

Sincerely,
Dr. Dennis P. Allen, Jr.

my favorite intro to complex analysis
This is a masterful treatment of the subject, including power series, integration, the homotopy version of cauchy's theorem, residue calculus, differential equations, harmonic functions, and intro to riemann surfaces.

i confess i do not recognize the book i read from the first review here however, as mine begins with formal power series and has rather little on several complex variables.I have both the 1963 hardback and the recent dover reprint and they are identical, but i have not seen the french version.

It is sobering that after 2 years not one person has even reacted to this review.Are todays students totally clueless about what books to learn from?I have a phd in math and am an internationally known researcher in math.give yourself a break and give my suggestions a try.how much do you have to lose on a book of this price?

if you doubt me i would recall that this was the book of choice at harvard in 1965 by the great john torrance tate.

a translation of a classic
This elegant little book by Henri Cantan covers both complex functions on one and several variables, and in that way (by the inclusion of several variables) it differs and stands out from most other books on complex variables at the beginning US-graduate level. It is a translation of an original French language version. I can recommend both the original and the translation. It is readable, and the exercises are plenty and excellent. Thanks to Dover, the translation is now readily available and cheap.

Cartan's book starts with complex numbers, power series, and a review of the standard complex functions of one variable, e.g., the exponential, and the complex logarithm. Then follow holomorphic functions, Taylor and Laurent expansions, singularities, Cauchy's theorems, residues, analytic continuation, lots of examples, and beautifully illustrated. Included are also geometric topics, elementary complex geometry, Mobius transformations, automorphisms, transformation groups, differential forms, harmonic and analytic functions, Riemann surfaces, and infinite products, and a brief chapter on conformal mappings.

The book is divided pretty evenly between one and several variables, with the second half being several variables. However each part can be read pretty much independently of the other.

The book in its French edition was published first in the 1950ties, and the first English edition in 1963, and then starting 1995 reprinted by Dover. It is suitable as a text for a course or as a supplement in a standard beginning graduate course in complex function theory. While it contains the standard elements in such a course, we note that a systematic treatment of power series comes relatively late, in Chapter 10, beginning on page 195 (halfway into the book.) Some readers might want to begin with that.

Of other Dover titles on the same subject, but considerably more elementary we recommend the books by Fisher, Volkovyskii et al, Silverman, Schwerdtfeger, and Flanigan. These books however only cover the case of a single variable. Review by Palle Jorgensen, August 5, 2006.

A good introduction
At first the book appeared to be too difficult. Indeed, it is designed for students with some familiarity with Algebra and Topology. However, the more I read the book, the better it appeared. It's chapter on integration is one of the best I've seen. It doesn't seem to cover much, but the addition of some facts from several variables is in very good taste.

Good and affordable.
Cartan's book on complex analysis is not brand new, but that does not matter as the subject itself has been "stabilized" for a long period of time. It is indeed good to see that this "lovely" book being available at the modest price of [price]. The fact that the author was among the founders of Bourbaki may intimidate some would-be readers, but you don't have to be worried. The treatment of the subject is no pedantic and quite accessible for beginners. ... Read more

Customer Reviews (2)

A wonderful book
For me this text is a joy and a delight. In the preface the authors remark that to acquire a thorough grasp of the subject requires hard work They assert the virtues of this book to be clarity of presentation, selection of topics, and interesting exercises. They express their hope that the book will help the student to become as enthusiastic about the subject as the authors are. In my case they achieve their goals.

Very many years ago I took complex analysis in grad school using the then-recent text by Ahlfors, and with a 100% Teutonic professor; I then found the subject boring. This book, however makes me enthusiastic. It is one of the few math texts I own that I like for bedtime reading, opening it to something of interest, or just to a random section or some exercises, and relaxing while reading as if it were an adventure novel. When I put it down, consequences trickle through my mind as I go to sleep. No, it's not an easy subject, but the authors make it an enthralling one, at least for me.

Very thorough, very challenging exercises.
This is not the easiest book on complex analysis to read, but nevertheless I really like it.If I had to use one word to describe it, it would be thorough.I have not read much beyond the first half of it, so my comments do not apply to the more advanced chapters.

The prose is sometimes clear, but at times you have to think very hard to get through it.Although there are a number of diagrams, I do not find them particularly helpful.The book does not move too fast, it actually moves quite slowly, but it explores a lot--it is very thorough.

This book has a ton of exercises, and some of them are very hard and very deep.I think the exercises are the best part of this book.This book makes me realize that a lot of other complex analysis textbooks do not have enough exercises, especially challenging ones.My favourite part are the exercises that explore counterexamples to converses of theorems.There are also a lot of great exercises involving infinite series.

I think this book would be most appropriate to someone who had already taken an undergraduate course in complex analysis and was taking a more advanced graduate course, or wanted to enrich their understanding on their own.This is a study text, not a reference text; it is ideal for learning and challenging a student.It is not concise, and it is harder to follow than the books by Lang, Newman & Bak, or Gamelin.However, I am convinced that someone reading this book would reach a deeper understanding of the subject than someone reading any of those other books. ... Read more

Product Description
Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 1 begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described in detail, and various applications of residues are included; analytic continuation is also introduced.

The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general. ... Read more

Product Description
Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers differentiation integration Cauchy's theorem and its consequences Laurent series and the residue theorem applications of contour integration conformal mappings and harmonic functions A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. ... Read more

Product Description
The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field.

The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster. ... Read more

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Product Description
This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study. ... Read more

Product Description
Complex Analysis with Mathematica offers a new way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos, and advanced conformal mapping. A CD is included which contains a live version of the book, and the Mathematica code enables the user to run computer experiments. ... Read more

Customer Reviews (1)

A true delight
What a wonderful and delightful book. The author has taken a well-worn topic and infused it with insight and energy. Best of all, the author communicates simply and clearly. He has brought graduate complex analysis to the masses; I wish that I had a book like this as an undergraduate. It is also a great read: the kind of pick you could pick up and go cover to cover with. However, you'll probably want to be at your keyboard trying out his many examples. The unique thing about this tome is that it is well-written, it is mathematically ambitious and it is an invaluable reference for how to use Mathematica. Also, as we have come to expect from Cambridge, this book has excellent production quality. ... Read more

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Product Description
Intended for the undergraduate student majoring in mathematics, physics or engineering, the Sixth Edition of Complex Analysis for Mathematics and Engineering continues to provide a comprehensive, student-friendly presentation of complex analysis. The authors strike a balance between the pure and applied aspects of the subject, and present concepts in a clear writing style that is appropriate for students at the junior/senior level. Through its thorough, accessible presentation and numerous applications, the sixth edition of this classic text allows students to work through even the most difficult proofs with ease. Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, the authors devote attention to important topics such as ensuring that required assumptions are met before using a theorem, confirming that algebraic operations are valid, and checking that formulas are not blindly applied. ... Read more

Customer Reviews (8)

Helpful Book
As a self-learner, I was looking for a self-contained book that would teach the fundamentals of complex analysis in a straight-forward manner without getting bogged down with a lot of advanced level mathematical jargon and proofs on every page.I was also looking for a book that would show how complex analysis is applied to various physical problems.I found all of this nicely packaged in this book.The explanations for the various topics were clear, with a lot of geometrical interpretations so that you could picture what was being discussed.I found the coverage of Riemann surfaces to be a good example of this approach.There are plenty of worked examples to help deepen your understanding of the material.The problems at the end of each chapter were not extremely difficult, yet helped to reinforce or extend the chapter's concepts.For a self-learner, this is a helpful approach.It not only builds understanding, but self-confidence.I found out about this book after trying to learn complex analysis with McMahon's book Complex Variables Demystified. I lost confidence in the ability of this book to provide clear explanations of the topics after discovering all of the serious errors contained within.I had to turn to the internet for clearer explanations, and found the website complement to this book.I was impressed with the website, so bought the book.I was not disappointed.

Complex Analysis for Mathematics and Engineering
This book was in great condition and the company worked well with me in the return of the book since it wasn't exactly what I needed.I would definately use them again.

Get your feet slightly damp in analysis
This book is a great way to ease into some more advanced topics in mathematics.For instance, within the first chapter you start to study topology of the complex field (mappings of sets of points, bounded sets, domains, etc).Of course none of this can be done until you establish the complex number system in terms of R which we are familiar with, and defining the arithmetic options and such.The construction of the complex field in terms of R and continually building off this idea the entire book was very fun and intuitive.It is a great help to read the semester before you take a more rigorous course in analysis, because it will give you a peak at its subtleties without beating you over the head with them.

An understandable presentation of complex analysis.
This book is useful for learning both the theorems and applications of complex functions.It is better organized and more up to date than other books I found in the library.The proofs and examples are complete and easy to understand and there are many well composed figures which help illustrate the concepts. I learned a lot about complex sequences and series and enjoyed the many practical examples like conformal mappings. The computer supplements for Maple and Mathematica look interesting. I can see how complex analysis is used in the real world.

Should be renamed Complex Analysis for Engineers
If you are engineering student, then you're going to love this book to death. If you are interested in pure mathematics, on the otherhand, then do not waste your time here. This book promotes absolutely no rigor whatsoever. I'm using this textbook for my complex analysis course right now, and I must say that this book is beyond boring. I have to force myself to read the book mainly to keep up with my class. I feel that doing rigorous mathematics gives the reader a sense of freedom and that they are free to do things they never thought was possible in the mathematical world. This book, on the otherhand, forces the reader to pretend like they are doing calculus I work. Been there, done that, time to move on.

Bottomline: Avoid this book if you love pure mathematics(if you have to use it for a complex analysis course, then pick up a supplmentary theoretical text that lets you enjoy the subject). ... Read more

Product Description

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.

The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.

This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works.

Product Description
This book is an outgrowth of lectures given at several occasions at the University of Göteborg and Chalmers University of Technology during the last ten years. Contrary to most introductory texts on complex analysis, it preassumes knowledge of basic analysis. This makes it possible to move rather quickly through the most fundamental material and to reach within a one-semester course some classical highlights such as Fatou theorems and some Nevanlinna theory, as well as more recent topics, for example the corona theorem and the H1-BMO duality. ... Read more

Product Description

In Risk Analysis of Complex and Uncertain Systems acknowledged risk authority Tony Cox shows all risk practitioners how Quantitative Risk Assessment (QRA) can be used to improve risk management decisions and policies. It develops and illustrates QRA methods for complex and uncertain biological, engineering, and social systems – systems that have behaviors that are just too complex to be modeled accurately in detail with high confidence – and shows how they can be applied to applications including assessing and managing risks from chemical carcinogens, antibiotic resistance, mad cow disease, terrorist attacks, and accidental or deliberate failures in telecommunications network infrastructure.  This book was written for a broad range of practitioners, including decision risk analysts, operations researchers and management scientists, quantitative policy analysts, economists, health and safety risk assessors, engineers, and modelers.

Customer Reviews (2)

Comprehensive and example-laden - Every issue is touched
I have used Cox's research in my own recent book, .He is a colleague who has written numerous articles on this topic and has combined those along with his practical experience to write this critical book.It touches on every major issue in the area of risk assessment - which includes many issues that other risk assessment authors either dare not touch or are simply unaware of.

The most impressive feature of this book is the litany of examples in literally every chapter.He draws on a wide spectrum of different fields including public health, airline safety, engineering risks and terrorism.It is an extremely comprehensive treatment of quantitative risk assessment methods and each method is backed up with practical applications.

For me, the most important part of this book is the large section Cox dedicates to "Avoiding Bad Risk Analysis".He systematically debunks what I think are the most popular methods in business today.I even used his phase "Worse than Useless" to describe such methods in my book (properly attributed, of course) because nothing else says it better.

But Cox doesn't just endorse every method used in quantitative risk assessment.He is careful to point out the potential flaws and proposes specific solution.Debunking these popular methods is the first step.The second step is adopting an improved quantitative approach to risk assessment.This book covers all of it.

Highly recommended.

real risk analysis
This is an excellent, approachable read for any risk manager; understanding its examples requires only elementary probability, statistics and calculus, though the foundations are much deeper.The author uses direct language, and does not hesitate to declare a fashionable risk analysis technique "worse than useless."The author shows how not to do risk analysis, using simple but devastating examples to illustrate the weaknesses of prioritized investments, subject matter expert opinion, risk matrices and qualitative risk assessments, and the independence assumption.Then, case studies present constructive examples of good practice.Refreshingly, this text clearly distinguishes between threats from Mother Nature, and those posed by an intelligent adversary.There is unevenness, because this is an edited ensemble of papers originally published in a variety of technical journals; however, this is also a strength, because the appeal and scholarship underlying biological, engineering, and social science examples is broad.This is not a how-to guide, and won't help fill in a blank page risk analysis; however, this is an excellent source for the skeptical consumer of contemporary risk management advice and products, and hopefully will have some influence with policy makers who are the source of simplistic and dangerous guidance.

Gerald G. Brown
Distinguished Professor of Operations Research
Naval Postgraduate School
National Academy of Engineering
INFORMS Fellow
... Read more

Product Description
A textbook presenting complex analysis in one variable in the context of modern mathematics, with connections to several theories and complex variables, including de Rhan theory and real analysis. Includes over 100 pages of exercises, problems, and examples, giving students ample practice. DLC: Functions of complex variables. ... Read more

Customer Reviews (1)

A great way to begin learning Complex Analysis
This book, like each lecture by Narasimhan that I have had the pleasure to hear, exhibits masterful understanding and exposition of the material.His proofs are extremely elegant, and it is always clear where he is going with the material.His writing flows very smoothly, and the addition of exercises to this edition is very helpful in the process of learning to prove things in the various areas covered in the chapter.He also does a great job of allowing one to make the connections between complex analysis and other fields of mathematics, and the notes at the end of each chapter offer interesting insight into the material such as various mathematicians involved in developing the topics and other areas of interest relative to the particular chapter.It is rare that an elementary book on complex analysis goes into further topics like several complex variables and complex manifolds, so if you are interested in learning complex analysis and preparing to extend to further related topics, this is the book for you. ... Read more

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Customer Reviews (2)

Just what I expected
The book was just as expected.Took a little long to be delivered, but overall I was satisfied.

Helpful but short
The Student Guild is helpful, but keep in mind that only the bulleted problems from Basic Complex Analysis are explained (only a few from each section).And the cost was a little high, expecially considering it's 135 pages. ... Read more