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Field name	Details
Dewey Class	515
Title	An Introduction to Classical Complex Analysis ([EBook]) : Vol. 1 / by Robert B. Burckel.
Author	Burckel, Robert B. , 1939-
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 1979.
Physical Details	570 pages : online resource.
Series	Mathematische Reihe, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften ; 64
ISBN	9783034893749
Contents note	0 Prerequisites and Preliminaries -- § 1 Set Theory -- § 2 Algebra -- § 3 The Battlefield -- § 4 Metric Spaces -- § 5 Limsup and All That -- § 6 Continuous Functions -- § 7 Calculus -- I Curves, Connectedness and Convexity -- § 1 Elementary Results on Connectedness -- § 2 Connectedness of Intervals, Curves and Convex Sets -- § 3 The Basic Connectedness Lemma -- § 4 Components and Compact Exhaustions -- § 5 Connectivity of a Set -- § 6 Extension Theorems -- Notes to Chapter I -- II (Complex) Derivative and (Curvilinear) Integrals -- § 1 Holomorphic and Harmonic Functions -- § 2 Integrals along Curves -- § 3 Differentiating under the Integral -- § 4 A Useful Sufficient Condition for Differentiability -- Notes to Chapter II -- III Power Series and the Exponential Function -- § 1 Introduction -- § 2 Power Series -- § 3 The Complex Exponential Function -- § 4 Bernoulli Polynomials, Numbers and Functions -- § 5 Cauchy’s Theorem Adumbrated -- § 6 Holomorphic Logarithms Previewed -- Notes to Chapter III -- IV The Index and some Plane Topology -- § 1 Introduction -- § 2 Curves Winding around Points -- § 3 Homotopy and the Index -- § 4 Existence of Continuous Logarithms -- § 5 The Jordan Curve Theorem -- § 6 Applications of the Foregoing Technology -- § 7 Continuous and Holomorphic Logarithms in Open Sets -- § 8 Simple Connectivity for Open Sets -- Notes to Chapter IV -- V Consequences of the Cauchy-Goursat Theorem—Maximum Principles and the Local Theory -- § 1 Goursat’s Lemma and Cauchy’s Theorem for Starlike Regions -- § 2 Maximum Principles -- § 3 The Dirichlet Problem for Disks -- § 4 Existence of Power Series Expansions -- § 5 Harmonic Majorization -- § 6 Uniqueness Theorems -- § 7 Local Theory -- Notes to Chapter V -- VI Schwarz’ Lemma and its Many Applications -- § 1 Schwarz’ Lemma and the Conformal Automorphisms of Disks -- § 2 Many-to-one Maps of Disks onto Disks -- § 3 Applications to Half-planes, Strips and Annuli -- § 4 The Theorem of CarathSodory, Julia, Wolff, et al -- § 5 Subordination -- Notes to Chapter VI -- VII Convergent Sequences of Holomorphic Functions -- § 1 Convergence in H(U) -- § 2 Applications of the Convergence Theorems; Boundedness Criteria -- § 3 Prescribing Zeros -- § 4 Elementary Iteration Theory -- Notes to Chapter VII -- VIII Polynomial and Rational Approximation—Runge Theory -- § 1 The Basic Integral Representation Theorem -- § 2 Applications to Approximation -- § 3 Other Applications of the Integral Representation -- § 4 Some Special Kinds of Approximation -- § 5 Carleman’s Approximation Theorem -- § 6 Harmonic Functions in a Half-plane -- Notes to Chapter VIII -- IX The Riemann Mapping Theorem -- § 1 Introduction -- § 2 The Proof of Caratheodory and Koebe -- § 3 Fejer and Riesz’ Proof -- § 4 Boundary Behavior for Jordan Regions -- § 5 A Few Applications of the Osgood-Taylor-Caratheodory Theorem -- § 6 More on Jordan Regions and Boundary Behavior -- § 7 Harmonic Functions and the General Dirichlet Problem -- § 8 The Dirichlet Problem and the Riemann Mapping Theorem -- Notes to Chapter IX -- X Simple and Double Connectivity -- § 1 Simple Connectivity -- § 2 Double Connectivity -- Notes to Chapter X -- XI Isolated Singularities -- § 1 Laurent Series and Classification of Singularities -- § 2 Rational Functions -- § 3 Isolated Singularities on the Circle of Convergence -- § 4 The Residue Theorem and Some Applications -- § 5 Specifying Principal Parts—Mittag-Leffler’s Theorem -- § 6 Meromorphic Functions -- § 7 Poisson’s Formula in an Annulus and Isolated Singularities of Harmonic Functions -- Notes to Chapter XI -- XII Omitted Values and Normal Families -- § 1 Logarithmic Means and Jensen’s Inequality -- § 2 Miranda’s Theorem -- § 3 Immediate Applications of Miranda -- §4 Normal Families and Julia’s Extension of Picard’s Great Theorem -- § 5 Sectorial Limit Theorems -- § 6 Applications to Iteration Theory -- § 7 Ostrowski’s Proof of Schottky’s Theorem -- Notes to Chapter XII -- Name Index -- Symbol Index -- Series Summed -- Integrals Evaluated.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-9374-9
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Burckel, Robert B. 1939- . Corporate Authors: SpringerLink (Online service) . Series: Mathematische Reihe, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften . Classification: 515 . 515 (DDC 20) .

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An Introduction to Classical Complex Analysis: Vol. 1

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