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An Introduction to Complex Analysis: Classical and Modern Approaches: Modern Analysis Series

Autor Wolfgang Tutschke, Harkrishan L. Vasudeva
en Limba Engleză Hardback – 25 iun 2004
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.
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Specificații

ISBN-13: 9781584884781
ISBN-10: 1584884789
Pagini: 476
Ilustrații: 52 b/w images and 1000 equations
Dimensiuni: 156 x 234 x 30 mm
Greutate: 1.04 kg
Ediția:New.
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Modern Analysis Series


Public țintă

Undergraduate

Cuprins

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.

Recenzii

"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

Notă biografică

Wolfgang Tutschke, Harkrishan L. Vasudeva

Descriere

An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis that relate to complex analysis, followed by brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches are also presented for comparison. Discussions include holomorphic functions, analytic continuation, isolated singularities, 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.