Complex Variables and Applications

by James Ward Brown, Ruel V. Churchill

This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text.

Genres: Mathematics, Textbooks, Nonfiction, Reference, Physics, Science, Technical

352 pages, Hardcover

First published December 1, 1960

Reviews

[Walter U. · Rating 5 out of 5]

This book was recommended to me by my advisor as a good intro/refresher for complex variables. According to him, back in his days this book was widely regarded as the gold standard for this subject. Now that I've had some time with it, I cannot find reason to disagree.

The exposition is clear, with just enough examples to get the point across. The themes are well organized and all major theorems are accompanied by their proofs, which is a godsend. The exercises offer plenty of opportunity to apply the material, and they typically range from very easy to rigorous proofs. Answers are provided for a select few, but PDFs of the student solution manual can be found on the interwebs.

As far as the background needed to understand the material, I'd say nothing higher than integral calculus is strictly necessary, although those students with a background in analysis should get the most out of it.

All in all, a great little book.

[James Swenson · Rating 4 out of 5]

OK, I'm giving it 4 stars now, but I'm going to teach from it for the first time this semester (Spring 2012). Let's see what I think in May....

[UPDATE] The course is finished; I now like the book slightly more than I did going in. The exercises provide good material for an undergraduate course.

[Milad · Rating 5 out of 5]

When you begin reading a definition or a theorem in this book, you're guided step by step in understanding the meaning and the proof.

And you need a very elementary knowledge of real analysis for this book.

[Ali Hasan · Rating 3 out of 5]

My math professor highly recommended this book, mentioning that it’s a bit more challenging than typical textbooks. Personally, I didn’t find the language particularly difficult. What made it harder for me was the way the book is structured. The style feels somewhat uncomfortable to read and analyze.

Maybe I’m not scholarly enough, or not attentive enough as an engineering student, but honestly, who cares? I think the book could have been better organized. Clearer chapter structures and more systematically arranged problems would make it more accessible and helpful for all types of students.

I’ve completed about 60% of it. I didn’t love it, but I didn’t hate it either.

On the positive side, if you’re truly determined to understand the material deeply, this book can be valuable. The problems are challenging, and although the explanations and exercises don’t always feel well synchronized, it still offers a rigorous way to learn concepts that are important throughout an engineering journey.

Overall, a solid 3/5 for me.

[Tomasduden · Rating 4 out of 5]

Mye complex varibles, men lite applications

[Erickson · Rating 5 out of 5]

I think it is really very good text for introductory complex analysis especially if you intend to learn it for applications, instead of, say, developing or becoming researcher in complex theory. For pure mathematics research, a better and more thorough text would be needed. However, for applications --- which is often the main focus of first course in complex analysis --- this book is excellent, with many exercises and the writing style is engaging and clear. I could review all essentials of the first seven chapters in mere two days if proofs are skipped and some examples really helped. Another text by Howie has similar accessibility albeit too short to be as useful if you are looking for examples.

Personally, if you have the time, I would recommend having this book either way, along with more rigorous text beside you if you need to pursue further.

[Abbey · Rating 2 out of 5]

not too bad overall, but I found myself looking for other texts to see if they explained concepts better quite a bit. needed clearer explanations in places.

[Joe Cole · Rating 5 out of 5]

This is a good reference on the subject of complex analysis. The author has included helpful methods for the analysis of singularities that I have not been able to find anywhere else.

[Rıdvan Erdem · Rating 4 out of 5]

bdfgdfdfd

[John · Rating 5 out of 5]

The best introduction to Complex Analysis that I have seen. The exposition is simplified when compared to many other texts, which allows the author to make the main ideas prominent instead of hiding them behind the peripheral details you'll find in many other books. As an example, homology and winding numbers are not mentioned at all, but when you'll see them in your next book/course, you'll have no problem understanding them if you handle the essential, major ideas such as multivalued (inverse) functions, an analytic function and its properties under differentiation, integration and expansion into series.

As an curuous vignette, Churchill proves the Cauchy's theorem using the Green's formula before going to proving or the usual way, which prepares the reader for the idea of the Cauchy-Riemann equations being a consequence of the Stokes theorem - not very many Complex Analysis books highlight this link between Differential Geometry and Complex Analysis.

I've tried many other books in the subject, and found Churchill's introduction the overwhelmingly best in the class.

[Robert · Rating 2 out of 5]

Could be a lot clearer

[Manoj Khatri · Rating 4 out of 5]

Tried many books, all missing something. Best as an introduction. Will not take you to places, though.

[Sezin Mutlu · Rating 4 out of 5]

HAV HAV HAV HAV HAYATIMI MAHVETTİN AMA İNCE BİR ZEVK DE ALDIM BUNDAN

[Tuvalu · Rating 5 out of 5]

goated textbook. covered the topics very well without going too much into the analysis. perfect for people who need to learn topics covered by complex analysis but dont need to be writing crazy analysis proofs.

[Adam Lantos · Rating 3 out of 5]

It's a pretty good book, but not really great and I didn't find it to be an interesting or exciting read. There are other books, like Zill's "A First Course on Complex Analysis", that are much better. In particular, I found that Churchill's and Brown's book lacked in intuitive explanations of the various concepts presented here; they rely more on just doing the calculations which is great for just learning how to work with Complex numbers. Moreover, I really didn't find the sections on applications of complex analysis to be that interesting, at least in comparison with other complex analysis textbooks.

[Thomas · Rating 2 out of 5]

I used this book for an undergraduate course, and I simply have a bad experience with it. Most of the sections preceding the problems are too wordy, as if the author is assuming the reader has no background in mathematics at all, and this wordy treatment actually makes it more confusing. I would recommend Complex Analysis in the Spirit of Lipman Bers or Complex Analysis by Freitag.

[Ahmed Abrar · Rating 2 out of 5]

It could be retitled as 'A Very Short Introduction to Complex Variables and Applications'. Without three-dimensional tinted images, it's very much onerous to conceive of complex plane and its four-dimensional dance i.e. projection. Such a small number of definitions, lemma or scanty derivations bemused me more.

[Salah Abuzaina · Rating 3 out of 5]

This book summarizes the main outlines of complex analysis, and the theory of functions of complex variables.It discusses complex analysis whithin various fields, such as : properties of complex numbers, mappings, elementary functions, series, analytic and harmonic functions and integrals.

[HikBook]

La convergencia del valor principal de una funcion no implica la convergencia de la integral impropia.
El valor principal de x existe pero la integral impropia de x no existe.

88 jordan's lemma
integral over a contourn converges to zero

[NumberLord · Rating 3 out of 5]

A decent book for learning complex analysis if you're an undergraduate. For graduate students, I would look elsewhere.

[Shabnam]

متغيرهاي مختلط و كاربردها
ترجمه:امير خسروي

[Nick Black · Rating 3 out of 5]

Got me through undergraduate Complex Anal, but I didn't really understand the stuff until reading Penrose. Uninspiring, but acceptable...for now.

[Hegy · Rating 4 out of 5]

هل في طريقة عرضه للموضوع

[Aktham · Rating 5 out of 5]

thankx

[Sumitava Nayak]

complex variable

[Punpun Pun]

good

[Kunaldeore]

comment

[Mustafa Tokatlı]

şl

[Qothrotun Nada · Rating 3 out of 5]

buku edisi ketujuh yang dipakai saat kuliah semester 3. mata kuliah varkom.

[Mohammed Al-Shaleli · Rating 5 out of 5]

great