
An Introduction to Complex Analysis
Classical and Modern Approaches
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 25. June 2004
Book
Hardback
476 pages
978-1-58488-478-1 (ISBN)
Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.
To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison.
Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison.
Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
Reviews / Votes
"Many things, which are briefly described in others books, in remarks or exercises, are given in full detail ... . [It] will please readers interested ... in applications as well as those who want to know how things really work and prefer deeper and more detailed treatment of the material. The book also contains more than 200 examples and 150 exercises. ... I recommend it for courses in complex function theory ... and also as a reference book."- EMS Newsletter, Dec. 2004
"... [A]bundant examples and 'hints' to aid readers [are provided]. Summing Up: Recommended. Upper-division undergraduates through professionals."
- CHOICE, March 2005, Vol. 42, No. 07
"For the unification of the structure of mathematical analysis as a whole, it is imperative to use results of real analysis when laying the foundations of complex analysis. This is done in the present book."
-Zentralblatt MATH
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Undergraduate
Illustrations
52 s/w Abbildungen
52 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 30 mm
Weight
878 gr
ISBN-13
978-1-58488-478-1 (9781584884781)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Wolfgang Tutschke | Harkrishan L. Vasudeva
An Introduction to Complex Analysis
Classical and Modern Approaches
E-Book
06/2004
1st Edition
Chapman & Hall/CRC
€204.99
Available for download

Wolfgang Tutschke | Harkrishan L. Vasudeva
An Introduction to Complex Analysis
Classical and Modern Approaches
E-Book
06/2004
Chapman and Hall
€205.99
Available for download
Persons
Wolfgang Tutschke, Harkrishan L. Vasudeva
Content
Preliminaries. The
Classical Approach. An Alternative Approach. Local Properties. Global Properties. Isolated Singularities. Homotopy. Residue Theory. Applications of Residue Calculus. Mapping Properties. Special Functions. Boundary Value Problems. References.
Classical Approach. An Alternative Approach. Local Properties. Global Properties. Isolated Singularities. Homotopy. Residue Theory. Applications of Residue Calculus. Mapping Properties. Special Functions. Boundary Value Problems. References.