Complex Variables with Applications [electronic resource] / by S. Ponnusamy, Herb Silverman.
By: Ponnusamy, S [author.].
Contributor(s): Silverman, Herb [author.]  SpringerLink (Online service).
Material type: TextPublisher: Boston, MA : Birkhäuser Boston, 2006Description: XIV, 514 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817645137.Subject(s): Functions of complex variables  Mathematics  Differential equations, partial  Number theory  Geometry  Engineering mathematics  Functions of a Complex Variable  Applications of Mathematics  Several Complex Variables and Analytic Spaces  Number Theory  Geometry  Mathematical and Computational EngineeringAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.9 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB1214 
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.
Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a twodimensional 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 prerequisite is a basic knowledge of advanced calculus. The presentation is also ideally suited for selfstudy.
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