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Basic treatment includes existence theorem for solutions of differential systems, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises.<BR>
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6 Rezensionen
16 von 16 Kunden fanden die folgende Rezension hilfreich
Good and affordable.
30. Mai 2001
Format:Taschenbuch
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.
12 von 12 Kunden fanden die folgende Rezension hilfreich
a translation of a classic
6. August 2006
Format:Taschenbuch
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.
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 von 9 Kunden fanden die folgende Rezension hilfreich
A good introduction
17. Januar 2002
Format:Taschenbuch
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.
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