Ebook: An Introduction to Classical Complex Analysis: Vol. 1

"This is, I believe, the first modern comprehensive treatise on its subject. The author appears to have read everything, he proves everything, and he has brought to light many interesting but generally forgotten results and methods. The book should be on the desk of everyone who might ever want to see a proof of anything from the basic theory...." (SIAM Review)

" ... An attractive, ingenious, and many time[s] humorous form increases the accessibility of the book...." (Zentralblatt für Mathematik)

"Professor Burckel is to be congratulated on writing such an excellent textbook.... this is certainly a book to give to a good student [who] would profit immensely from it...." (Bulletin London Mathematical Society)

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Content:
Front Matter....Pages 1-12
Prerequisites and Preliminaries....Pages 13-21
Curves, Connectedness and Convexity....Pages 22-40
(Complex) Derivative and (Curvilinear) Integrals....Pages 41-52
Power Series and the Exponential Function....Pages 53-82
The Index and Some Plane Topology....Pages 83-119
Consequences of the Cauchy—Goursat Theorem—Maximum Principles and the Local Theory....Pages 120-190
Schwarz’ Lemma and its Many Applications....Pages 191-217
Convergent Sequences of Holomorphic Functions....Pages 218-255
Polynomial and Rational Approximation—Runge Theory....Pages 256-292
The Riemann Mapping Theorem....Pages 293-343
Simple and Double Connectivity....Pages 344-358
Isolated Singularities....Pages 359-410
Omitted Values and Normal Families....Pages 411-461
Erratum to: The Index and Some Plane Topology....Pages 571-571
Erratum to: Consequences of the Cauchy—Goursat Theorem—Maximum Principles and the Local Theory....Pages 571-571
Erratum to: Schwarz’ Lemma and its Many Applications....Pages 571-571
Erratum to: Convergent Sequences of Holomorphic Functions....Pages 571-571
Erratum to: Polynomial and Rational Approximation—Runge Theory....Pages 571-571
Erratum to: The Riemann Mapping Theorem....Pages 571-571
Erratum to: Simple and Double Connectivity....Pages 571-571
Erratum to: Isolated Singularities....Pages 571-571
Erratum to: Omitted Values and Normal Families....Pages 571-571
Erratum....Pages 571-571
Back Matter....Pages 462-570

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Content:
Front Matter....Pages 1-12
Prerequisites and Preliminaries....Pages 13-21
Curves, Connectedness and Convexity....Pages 22-40
(Complex) Derivative and (Curvilinear) Integrals....Pages 41-52
Power Series and the Exponential Function....Pages 53-82
The Index and Some Plane Topology....Pages 83-119
Consequences of the Cauchy—Goursat Theorem—Maximum Principles and the Local Theory....Pages 120-190
Schwarz’ Lemma and its Many Applications....Pages 191-217
Convergent Sequences of Holomorphic Functions....Pages 218-255
Polynomial and Rational Approximation—Runge Theory....Pages 256-292
The Riemann Mapping Theorem....Pages 293-343
Simple and Double Connectivity....Pages 344-358
Isolated Singularities....Pages 359-410
Omitted Values and Normal Families....Pages 411-461
Erratum to: The Index and Some Plane Topology....Pages 571-571
Erratum to: Consequences of the Cauchy—Goursat Theorem—Maximum Principles and the Local Theory....Pages 571-571
Erratum to: Schwarz’ Lemma and its Many Applications....Pages 571-571
Erratum to: Convergent Sequences of Holomorphic Functions....Pages 571-571
Erratum to: Polynomial and Rational Approximation—Runge Theory....Pages 571-571
Erratum to: The Riemann Mapping Theorem....Pages 571-571
Erratum to: Simple and Double Connectivity....Pages 571-571
Erratum to: Isolated Singularities....Pages 571-571
Erratum to: Omitted Values and Normal Families....Pages 571-571
Erratum....Pages 571-571
Back Matter....Pages 462-570
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