Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) [Paperback]

Henri Cartan (Author)

Book Description

ISBN-10: 0486685438 | ISBN-13: 978-0486685434 | Publication Date: July 6, 1995

Basic treatment of the 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 theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. Exercises. 1973 edition.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: French

Product Details

• Paperback: 228 pages
• Publisher: Dover Publications (July 6, 1995)
• Language: English
• ISBN-10: 0486685438
• ISBN-13: 978-0486685434
• Product Dimensions: 8.5 x 5.4 x 0.5 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #466,091 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

16 of 16 people found the following review helpful:

4.0 out of 5 stars Good and affordable., May 29, 2001

By A Customer

This review is from: Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) (Paperback)

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.

11 of 11 people found the following review helpful:

5.0 out of 5 stars a translation of a classic, August 5, 2006

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) (Paperback)

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.

8 of 9 people found the following review helpful:

5.0 out of 5 stars A good introduction, January 16, 2002

By 

"boian" (Madison, WI) - See all my reviews

This review is from: Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) (Paperback)

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.