Handbook of complex variables (Book, 1999) [WorldCat.org]
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Handbook of complex variables

Author: Steven G Krantz
Publisher: Boston, Mass. : Birkhäuser, ©1999.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Handbook of Complex Variables is a reference work for scientists and engineers who need to know and use essential information and methods involving complex variables and analysis. Its focus is on basic concepts and informational tools for mathematical "practice": solving problems in applied mathematics, science, and engineering." "This handbook is a reference and authoritative resource for all professionals,  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Steven G Krantz
ISBN: 0817640118 9780817640118 3764340118 9783764340117
OCLC Number: 40964730
Description: xxiv, 290 pages : illustrations ; 24 cm
Contents: 1. The Complex Plane. 1.1. Complex Arithmetic. 1.2. The Exponential and Applications. 1.3. Holomorphic Functions. 1.4. The Relationship of Holomorphic and Harmonic Functions --
2. Complex Line Integrals. 2.1. Real and Complex Line Integrals. 2.2. Complex Differentiability and Conformality. 2.3. The Cauchy Integral Theorem and Formula. 2.4. A Coda on the Limitations of the Cauchy Integral Formula --
3. Applications of the Cauchy Theory. 3.1. The Derivatives of a Holomorphic Function. 3.2. The Zeros of Holomorphic Function --
4. Isolated Singularities and Laurent Series. 4.1. The Behavior of a Holomorphic Function near an Isolated Singularity. 4.2. Expansion around Singular Points. 4.3. Examples of Laurent Expansions. 4.4. The Calculus of Residues. 4.5. Applications to the Calculation of Definite Integrals and Sums. 4.6. Meromorphic Functions and Singularities at Infinity --
5. The Argument Principle. 5.1. Counting Zeros and Poles. 5.2. The Local Geometry of Holomorphic Functions. 5.3. Further Results on the Zeros of Holomorphic Functions. 5.4. The Maximum Principle. 5.5. The Schwarz Lemma --
6. The Geometric Theory of Holomorphic Functions. 6.1. The Idea of a Conformal Mapping. 6.2. Conformal Mappings of the Unit Disc. 6.3. Linear Fractional Transformations. 6.4. The Riemann Mapping Theorem. 6.5. Conformal Mappings of Annuli --
7. Harmonic Functions. 7.1. Basic Properties of Harmonic Functions. 7.2. The Maximum Principle and the Mean Value Property. 7.3. The Poisson Integral Formula. 7.4. Regularity of Harmonic Functions. 7.5. The Schwarz Reflection Principle. 7.6. Harnack's Principle. 7.7. The Dirichlet Problem and Subharmonic Functions. 7.8. The General Solution of the Dirichlet Problem --
8. Infinite Series and Products. 8.1. Basic Concepts Concerning Infinite Sums and Products. 8.2. The Weierstrass Factorization Theorem. 8.3. The Theorems of Weierstrass and Mittag-Leffler. 8.4. Normal Families --
9. Applications of Infinite Sums and Products. 9.1. Jensen's Formula and an Introduction to Blaschke Products. 9.2. The Hadamard Gap Theorem. 9.3. Entire Functions of Finite Order --
10. Analytic Continuation. 10.1. Definition of an Analytic Function Element. 10.2. Analytic Continuation along a Curve. 10.3. The Monodromy Theorem. 10.4. The Idea of Riemann Surface. 10.5. Picard's Theorems --
11. Rational Approximation Theory. 11.1. Runge's Theorem. 11.2. Mergelyan's Theorem --
12. Special Classes of Holomorphic Functions. 12.1. Schlicht Functions and the Bieberbach Conjecture. 12.2. Extension to the Boundary of Conformal Mappings. 12.3. Hardy Spaces --
13. Special Functions. 13.0. Introduction. 13.1. The Gamma and Beta Functions. 13.2. Riemann's Zeta Function. 13.3. Some Counting Functions and a Few Technical Lemmas --
14. Applications that Depend on Conformal Mapping. 14.1. Conformal Mapping. 14.2. Application of Conformal Mapping to the Dirichlet Problem. 14.3. Physical Examples Solved by Means of Conformal Mapping. 14.4. Numerical Techniques of Conformal Mapping --
15. Transform Theory. 15.0. Introductory Remarks. 15.1. Fourier Series. 15.2. The Fourier Transform. 15.3. The Laplace Transform. 15.4. The z-Transform --
16. Computer Packages for Studying Complex Variables. 16.0. Introductory Remarks. 16.1. The Software Packages --
Glossary of Terms from Complex Variable Theory and Analysis --
Table of Laplace Transforms.
Responsibility: Steven G. Krantz.

Abstract:

This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. This book is a handy com pendium of  Read more...

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"This modern book can be warmly recommended to mathematicians as well as to users of applied texts in complex analysis; in particular it will be useful to students preparing for an examination in the Read more...

 
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