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Complex Variables with Applications
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Complex Variables with Applications

Complex Variables with Applications

S. Ponnusamy, Herb Silverman

528 pages, parution le 01/11/2006

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

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