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Complex Variables and Applications 8th Edition

by James Brown (Author), Ruel Churchill (Author)

4.3 226 ratings

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Complex Variables and Applications (Brown and Churchill)
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This text serves as an introductory course in the theory and application of functions of a complex variable. The text is designed to develop the theory that is prominent in applications of the subject. Readers will find a special emphasis given to the application of residues and conformal mappings.

ISBN-10

0073051942
ISBN-13

978-0073051949
Edition

8th
Publisher

McGraw-Hill
Publication date

January 10, 2008
Language

English
Dimensions

6.5 x 0.8 x 9.3 inches
Print length

468 pages
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Editorial Reviews

About the Author

Churchill, Professor Emeritus of Mathematics, University of Michigan.

Product details

Publisher ‏ : ‎ McGraw-Hill; 8th edition (January 10, 2008)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 468 pages
ISBN-10 ‏ : ‎ 0073051942
ISBN-13 ‏ : ‎ 978-0073051949
Item Weight ‏ : ‎ 1.7 pounds
Dimensions ‏ : ‎ 6.5 x 0.8 x 9.3 inches

Best Sellers Rank: #1,242,316 in Books (See Top 100 in Books)
- #160 in Functional Analysis Mathematics
- #641 in Mathematical Analysis (Books)
- #1,075 in Calculus (Books)

Customer Reviews:
4.3 226 ratings

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Customer reviews

4.3 out of 5

226 global ratings

How customer reviews and ratings work

Customers say

Customers disagree on the computational complexity. Some find the book a decent intro to complex analysis, while others say it's very light on applications. They also disagree on text quality, with some finding it works fine, while other find the writing needlessly complicated and the examples aren't explained well.

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Computational complexity Text quality

12 customers mention "Computational complexity"7 positive5 negative

Customers are mixed about the computational complexity of the book. Some find the exercises in the text very helpful and the book excels at making you computationally efficient in the complex plane. However, others say that the book is very light on applications of complex analysis, the examples aren't explained well, and the examples feel disorganized and nebulous. Some customers also mention that some of the problems are not straight forward and require much thinking.

"...Fast-paced and packed full of information, I thought it was an overall good textbook...." Read more

"...There are plenty of problems for first time analysis students (like myself) and plenty of work-out problems of varying difficulty...." Read more

"...The exercises themselves are quite frequently guided with hints as to how to proceed (particularly with proofs) or accompanied by answers to enable..." Read more

"...The book is very light on applications of complex analysis, but it's in-depth enough and without being overwhelming in its rigour or inscrutable..." Read more

7 customers mention "Text quality"4 positive3 negative

Customers have mixed opinions about the text quality. Some find the writing needlessly complicated and the examples aren't explained well. They also say the figures are missing and the equations are unreadable.

"What can I say? It's a math book and it does it's job just fine...." Read more

".../corollary/lemma" in front of them, but several are typeset to take up several lines so that, after the first paragraph break, it's easy to miss..." Read more

"Nice product and good function" Read more

"Good text for first time analysis course..." Read more

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Fred Burroughs

For non-mathematicians who want a great complex analysis book

Reviewed in the United States on February 8, 2015

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Comprehensive and easy to understand, this deceptively slim book will never be leaving my collection. From basis algebra to series and methods of integration and conformal mapping, this book covers it all and explains it in small little chunks so that you are never overwhelmed by new material. One new thing is taught, then some problems, then another thing, then some problems, etc. You can advance through it fairly quickly depending on how many of the exercises you plan to do. The material in this book is necessary to really grasp complex analysis. It will not do to simply have a copy of Arfken or some other mathematical methods book that has a chapter or two on complex analysis.

The book is very light on applications of complex analysis, but it's in-depth enough and without being overwhelming in its rigour or inscrutable notation that it's very useful for science and engineering majors to have.

6 people found this helpful

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H. G. Harmon

One of The Best Math Textbooks Ever

Reviewed in the United States on April 28, 2011

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For me, this book serves as a firm grounding in the basics, before moving on to the doctoral prelim sequence in Complex Variables. It's also easy to see how it can support a self-contained course for those who will never need more than the fundamentals. And yes, as is so often said falsely of other books, this one is "ideal for self-study."

Generally, the proofs flow easily: You can read them start to finish without all the inordinate cross-referencing of prior Lemmas, Corollaries, and Theorems that plagues lesser textbooks. Enough of that, and you might as well leave the proof in question for an exercise! I don't see much sacrificing of rigor, either; just a more conversational style with ordinary but precise language standing in for quantifiers and notation that require more mathematical maturity.

A few seemingly minor but actually major points regarding style and presentation: The print is large enough to read without squinting to discern the difference between an i and a j, especially with double-indexing. Also, the text is not compacted onto the page; they leave space---and hence time---to digest a sentence before moving to the next. You never get the feeling that you're being inundated with more info than you could possibly absorb and retain. The illustrations are always drawn to an appropriate scale, and do indeed clarify rather than obfuscate. I think everyone knows, if only implicitly, what a difference these considerations make.

All in all, we get just the right topics covered in just the right depth in a textbook of just the right size. A true modern classic!

13 people found this helpful

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Tyler Soelberg

A thorough introduction to Complex Analysis

Reviewed in the United States on December 13, 2010

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What can I say? It's a math book and it does it's job just fine. It does feel slightly rushed, but I suppose the upside of that is that it doesn't ever really belabor the point.
Fast-paced and packed full of information, I thought it was an overall good textbook. The format is probably a little unfamiliar to most who haven't had courses on this level before, but it's nothing that you can't get used to (there are something like 12 chapters and 128 sections, but sections are presented two or three at a time, followed by some exercises).

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Kilcun

Good text for first time analysis course

Reviewed in the United States on November 17, 2011

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This book is pretty good to read and has great examples and problems. There are plenty of problems for first time analysis students (like myself) and plenty of work-out problems of varying difficulty.

Kind of odd that the section numbers don't restart with the new chapters so you end at section 100 something, but it's not really a big deal.

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Takuto Sato

Quick shipping, beautiful book.

Reviewed in the United States on June 19, 2021

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Quick shipping, beautiful book. Thank you.

Reviewed in the United States on May 19, 2008

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I purchased this book because the undergraduate course I took in complex analysis was taught by a professor who preferred to use Schaum's Outlines: Complex Variables (With an Introduction to Conformal Mapping and Its Applications) accompanied by some fabulous lectures. I didn't save my lecture notes, though, and I wanted a more thorough refresher in the subject than Schaum's can give. So, my qualifications when turning to this text are the following: undergraduate degree in math, previous experience with complex analysis, more extensive experience with real analysis, very recent review of multivariable calculus (which I mention because of the numerous parallels between some of the line integral theorems and contour integrals in the complex plane).

When I first picked up the book, it wasn't quite what I hoped for. Very short sections are divided into well-organized chapters. The sections themselves are hit-or-miss in terms of both depth and breadth of material. Some sections deal with a topic that seems meaty enough to warrant its own treatment (branch cuts and branch points) but without going into anything near the detail necessary to use the concept; others devote an entire section to a single theorem (Cauchy-Goursat) and another section to its proof; others combine several new ideas in one section devoted to treating a larger concept, the way most mathematics texts do. These sections are, unfortunately, few and far-between. In skimming superficially over an important topic or ponderously plodding through a single theorem without tying it to other material, the authors have created a book that feels disorganized and nebulous.

For my purposes--review of a subject with which I am already passingly familiar--this text works fine. I can see connections before they're introduced because I already know where the theory is headed, and my previous experience with mathematics makes it easier to see how things fit into place in the larger framework of analysis. But I have to wonder how an undergraduate with no previous experience in complex analysis would fare using this text. Concepts are introduced before they're used, and some material that I thought was pretty complex (pardon the pun, har har) is glossed over as if it were completely obvious.

The poor organization and layout contributes to the difficulty in comprehension. While the chapters are well-defined, and the sections are at least labeled by topic and numbered, I don't see how you could find your way through this text without copious highlighting. Theorems are offset with a nice bold "theorem/corollary/lemma" in front of them, but several are typeset to take up several lines so that, after the first paragraph break, it's easy to miss where the theorem ends and the discussion begins. The proofs are even worse. I never thought I'd yearn so desperately for three simple letters, but QEDs are completely missing from this text. Proofs go on for paragraphs, often interrupted by figures or even examples, without any sign from the layout that a conclusion has been reached or a new topic begun. Figures are often useful but poorly placed, so that the material referencing them is on a totally different portion of the page. Some theorems are stated more conversationally than elegantly, but at least that means I get to practice rephrasing in my notes.

The exercises in this text are very helpful. Examples are interspersed with the theory, often providing immediate applications and almost always assisting with the exercises at the end of the section. The exercises themselves are quite frequently guided with hints as to how to proceed (particularly with proofs) or accompanied by answers to enable work-checking. The progression of exercises is also very natural, working from simpler concepts to more advanced ones in a way that doesn't overwhelm the student.

Generally, I would recommend this book to someone hoping to review a subject that they already have some understanding of. Enough of the theory is obtuse enough that I wouldn't recommend it to someone who was looking for something to help them better understand the subject, but, unfortunately, I also can't think of a BETTER text. Overall, this book has no killing flaws. It does what it sets out to do. I just can't imagine how the eighth edition manages to have organizational flaws and skimpy detail after seven previous editions for students to complain about.

16 people found this helpful

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Crackle

Good book at a good price

Reviewed in the United States on April 9, 2021

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When you need this edition, you need it!

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Top reviews from other countries

chandu naik

Worthy a buy.

Reviewed in India on August 24, 2021

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The packing of the product is very good. The paper quality and book condition are excellent 👌👌. Coming to the content it contains the chapters required by a engineering student that are explained in good way with different examples and exercises. If you are any student in NIT , IIT you can definitely buy it .

One person found this helpful

S.M.

Nice

Reviewed in India on April 28, 2021

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Good book.

Shreshtha

Should give a try

Reviewed in India on March 13, 2020

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I recommend it for complex analysis because it has the perfect range, neither too hard that one would find difficult, nor too easy that skips important topics. Engineering mathematics book is also good, has plenty questions. But if you are a maths student and find the classics tough, like me, do read this one.

5 people found this helpful

Sandeep pramanik

Complex best

Reviewed in India on December 24, 2020

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Fresh new book good to see first time. And contents are really good that's why I purchased.

Arya

Amazing

Reviewed in India on January 8, 2021

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