Complex Variables with Applications

S. Ponnusamy, Herb Silverman

528 pages, parution le 01/11/2006

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Résumé

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions.

The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination.

The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequistite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.

Written for: Advanced undergraduates in mathematics, science and engineering

Sommaire

Algebraic and Geometric Preliminaries
Topological and Analytic Preliminaries
Bilinear Transformations and Mappings
Elementary Functions
Analytic Functions
Power Series
Complex Integration and Cauchy's Theorem
Applications of Cauchy's Theorem
Laurent Series and the Residue Theorem
Harmonic Functions
Conformal Mapping and the Riemann Mapping Theorem
Entire and Meromorphic Functions
Analytic Continuation
Applications
References
Index of Special Notations
Hints for Selected Questions and Exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	S. Ponnusamy, Herb Silverman
Parution	01/11/2006
Nb. de pages	528
Format	16 x 24
Couverture	Relié
Poids	865g
Intérieur	Noir et Blanc
EAN13	9780817644574
ISBN13	978-0-8176-4457-4