Complex Variables with Applications

Name: Complex Variables with Applications
Availability: InStock
ISBN: 9780817644574

ISBN-10: 0817644571

ISBN-13: 9780817644574

Edition: 2006

Authors: S. Ponnusamy, Herb Silverman

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Description:

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,…

Book details

List price: $99.99
Copyright year: 2006
Publisher: Birkhï¿½user Boston
Publication date: 9/13/2006
Binding: Hardcover
Pages: 514
Size: 6.10" wide x 9.25" long x 0.44" tall
Weight: 1.892
Language: English



Preface



Algebraic and Geometric Preliminaries



The Complex Field



Rectangular Representation



Polar Representation



Topological and Analytic Preliminaries



Point Sets in the Plane



Sequences



Compactness



Stereographic Projection



Continuity



Bilinear Transformations and Mappings



Basic Mappings



Linear Fractional Transformations



Other Mappings



Elementary Functions



The Exponential Function



Mapping Properties



The Logarithmic Function



Complex Exponents



Analytic Functions



Cauchy-Riemann Equation



Analyticity



Harmonic Functions



Power Series



Sequences Revisited



Uniform Convergence



Maclaurin and Taylor Series



Operations on Power Series



Complex Integration and Cauchy's Theorem



Curves



Parameterizations



Line Integrals



Cauchy's Theorem



Applications of Cauchy's Theorem



Cauchy's Integral Formula



Cauchy's Inequality and Applications



Maximum Modulus Theorem



Laurent Series and the Residue Theorem



Laurent Series



Classification of Singularities



Evaluation of Real Integrals



Argument Principle



Harmonic Functions



Comparison with Analytic Functions



Poisson Integral Formula



Positive Harmonic Functions



Conformal Mapping and the Riemann Mapping Theorem



Conformal Mappings



Normal Families



Riemann Mapping Theorem



The Class S



Entire and Meromorphic Functions



Infinite Products



Weierstrass' Product Theorem



Mittag-Leffler Theorem



Analytic Continuation



Basic Concepts



Special Functions


References and Further Reading


Index of Special Notations


Index


Hints for Selected Questions and Exercises