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Complex Analysis

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ISBN-10: 0521809371

ISBN-13: 9780521809375

Edition: 2006

Authors: Kunihiko Kodaira, A. F. Beardon, T. K. Carne, A. Sevenster

List price: $109.99
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Description:

Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem, and analytic functions on a Riemann surface. Including many problems and examples, this text is useful for a course in complex analysis.
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Book details

List price: $109.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 8/23/2007
Binding: Hardcover
Pages: 416
Size: 5.50" wide x 9.50" long x 1.00" tall
Weight: 1.496

Preface
Holomorphic functions
Holomorphic functions
The complex plane
Functions of a complex variable
Holomorphic functions
Power series
Series whose terms are functions
Power series
Integrals
Curves
Integrals
Cauchy's integral formula for circles
Power series expansions
Properties of holomorphic functions
mth-order derivatives
Limits of sequences of holomorphic functions
The Mean Value Theorem and the maximum principle
Isolated singularities
Entire functions
Cauchy's Theorem
Piecewise smooth curves
Smooth Jordan curves
Boundaries of bounded closed regions
Cellular decomposition
Calls
Cellular decomposition
Cauchy's Theorem
Cauchy's Theorem
Cauchy's integral formula
Residues
Evaluation of definite integrals
Differentiability and homology
Conformal mappings
Conformal mappings
The Riemann sphere
The Riemann sphere
Holomorphic functions with an isolated singularity at [infinity]
Local coordinates
Homogeneous coordinates
Linear fractional transformations
Linear fractional transformations
Cross ratio
Elementary conformal mappings
Analytic continuation
Analytic continuation
Analytic continuation
Analytic continuation by expansion in power series
Analytic continuation along curves
Analytic continuation by integrals
Cauchy's Theorem (continued)
Riemann's Mapping Theorem
Riemann's Mapping Theorem
Correspondence of boundaries
The principle of reflection
The principle of reflection
Modular functions
Picard's Theorem
The Schwarz-Christoffel formula
Riemann surfaces
Differential forms
Differential forms
Line integrals
Harmonic forms
Harmonic functions
Riemann surfaces
Hausdorff spaces
Definition of Riemann surfaces
Differential forms on a Riemann surface
Differential forms
Line integrals
Locally finite open coverings
Partition of unity
Green's Theorem
Dirichlet's Principle
Inner product and norm
Dirichlet's Priniciple
Analytic functions
The structure of Riemann surfaces
Planar Riemann surfaces
Planar Riemann surfaces
Simply connected Riemann surfaces
Multiply connected regions
Compact Riemann surfaces
Cohomology groups
Structure of compact Riemann surfaces
Homology groups
Analytic functions on a closed Riemann surface
Abelian differentials of the first kind
Harmonic 1-forms of the first kind
Abelian differential of the first kind
Abelian differentials of the second and third kind
Meromorphic functions
Abelian differentials of the second and third kind
The Riemann-Roch Theorem
Existence Theorem
The Riemann-Roch Theorem
Abel's Theorem
Existence Theorem
Abel's Theorem
Problems
References
Index