Complex Variables and Applications [Hardcover]

James Ward Brown (Author), Ruel V. Churchill (Author)

Book Description

ISBN-10: 0079121470 | ISBN-13: 978-0079121479 | Publication Date: October 1, 1995 | Edition: 6

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.

Product Details

• Hardcover: 352 pages
• Publisher: McGraw-Hill Science/Engineering/Math; 6 edition (October 1, 1995)
• Language: English
• ISBN-10: 0079121470
• ISBN-13: 978-0079121479
• Product Dimensions: 9.6 x 6.6 x 1 inches
• Shipping Weight: 1.6 pounds
• Average Customer Review: 3.9 out of 5 stars  See all reviews (47 customer reviews)
• Amazon Best Sellers Rank: #251,748 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

30 of 31 people found the following review helpful:

5.0 out of 5 stars Very clear, great for learning and understanding quickly, a bit slow at times, June 15, 2006

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
(REAL NAME)   

This review is from: Complex Variables and Applications (Churchill-Brown Series) (Hardcover)

This book is simply clearer than any other complex analysis book I've read, although it's not particularly advanced or concise.

This book is a great text for undergraduates studying complex analysis for the first time. It does not assume a strong background in rigorous analysis, making the material accessible to a wider audience.

At times I find that this book moves a bit slow for my personal taste, but what it loses in speed it makes up for in clarity. The explanations are always clear. I find that I never get stuck in a proof in this book. If there is a certain topic that I absolutely must understand, and I want to understand in a straightforward, useful way, as quick as possible, I turn to this book.

I would recommend this book for self-study as well as a textbook at the introductory level. It is not a particularly advanced book, and is not comprehensive as a reference for more advanced students, nor would it be a great choice for a graduate or advanced course.

39 of 43 people found the following review helpful:

5.0 out of 5 stars Excellent intro. to complex analysis!, June 18, 2004

By 

Anthony - See all my reviews

This review is from: Complex Variables and Applications : Macintosh (Churchill-Brown Series) (Hardcover)

This course was my first exposure to the mathematical field of analysis at the undergraduate level, and our school ditched Gamelin's book used two years ago in favor of this book. Just to give you an idea of the difference a book makes (it was the same teacher for both courses, mind you): when Gamelin was used, EVERYONE dropped out of the course; when Brown/Churchill was used, only one person dropped the course and half the class received A's!

Truly, this is a remarkable shift, and this book had a lot to do with it. I thought the organization was flawless (note: you will have to go through the book in order, as many examples depend on previous material), and starting from the beginning with the definition of a complex number was definitely the way to go, as about 1/3 of my class had never seen a complex number before. I loved the fact that there were many examples worked out (never explicitly showing people how to do the end-of-section exercises, but showing them the methods for where to go) and the major theorems were alloted many pages for clear proofs with diagrams and detailed explanations (an entire section was devoted to a proof of the Cauchy-Goursat theorem!). Also, the choices of problems were superb, with some routine exercises meant to get you thinking along the right tracks followed by some very difficult ones. Basically, enough to challenge even the ablest math student, but enough for the average one to get a grasp on the concepts as well.

The book also provides an advantage for the instructor as to what applications to teach. Granted, chapters 1-6 cover almost all the theory, but 7-12 are all applications (7 is "usually" considered theoretical as well, but it is called "applications of residues!") in physics, advanced calculus and geometry, and engineering. So, a professor could choose to emphasize only the theoretical parts and save the apps. for independent study (which my prof. did) or could teach the relevant theories coupled with some of the applications (conformal mapping with fluid flow and heat flow, for example). It truly is a versatile book.

I noticed a complaint on here about not having enough examples or worked-out proofs. Well, to that individual (and any others who might be having the same problem), this book is meant for an upper-level undergraduate course, which means that there are going to be less examples worked out in great detail, the proofs may just be thumbnail sketches, and the problems will not have a quick reference page in the chapter for a formula or method like in calculus, for example; even though the book is versatile, a lot of the learning still falls on the student's shoulders.

My one and only gripe is that the book didn't take a lot of time to spell out how to perform a delta-epsilon proof for limits, which is one of the basic proofs in analysis. But, luckily, I had a very patient instructor who was willing to walk it through with me (most of the rest of the class had already had real analysis, so they didn't need to go over it). But, still, it's not enough to take it down a star, in my opinion.

They say this book is among the canon of undergraduate mathematics, and I can certainly see why. What a great introduction to complex analysis! This book will definitely be accompanying me to grad school!

26 of 30 people found the following review helpful:

5.0 out of 5 stars One of the best math textbooks I've ever read, February 15, 2002

By 

Todd Ebert (Long Beach California) - See all my reviews

This review is from: Complex Variables and Applications (Churchill-Brown Series) (Hardcover)

I read this book in preparation for an analysis qualifying exam, and found that the examples, exercises, and explanations provided made the entire subject seem both easy and interesting. For a beginning student of complex analysis, I do not see any better option. Moreover, I believe every future mathematics-book author should study this book as an exercise on "what to do". Finally part II of Lang's "Complex Analysis" has alot of interesting advanced material related to geometric function theory, and would make a good follow-up to this book.