Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorBurckel, Robert B. author
TitleAn Introduction to Classical Complex Analysis [electronic resource] : Vol. 1 / by Robert B. Burckel
ImprintBasel : Birkhรคuser Basel, 1979
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9374-9
Descript 570 p. online resource

CONTENT

0 Prerequisites and Preliminaries -- ยง 1 Set Theory -- ยง 2 Algebra -- ยง 3 The Battlefield -- ยง 4 Metric Spaces -- ยง 5 Limsup and All That -- ยง 6 Continuous Functions -- ยง 7 Calculus -- I Curves, Connectedness and Convexity -- ยง 1 Elementary Results on Connectedness -- ยง 2 Connectedness of Intervals, Curves and Convex Sets -- ยง 3 The Basic Connectedness Lemma -- ยง 4 Components and Compact Exhaustions -- ยง 5 Connectivity of a Set -- ยง 6 Extension Theorems -- Notes to Chapter I -- II (Complex) Derivative and (Curvilinear) Integrals -- ยง 1 Holomorphic and Harmonic Functions -- ยง 2 Integrals along Curves -- ยง 3 Differentiating under the Integral -- ยง 4 A Useful Sufficient Condition for Differentiability -- Notes to Chapter II -- III Power Series and the Exponential Function -- ยง 1 Introduction -- ยง 2 Power Series -- ยง 3 The Complex Exponential Function -- ยง 4 Bernoulli Polynomials, Numbers and Functions -- ยง 5 Cauchyโ{128}{153}s Theorem Adumbrated -- ยง 6 Holomorphic Logarithms Previewed -- Notes to Chapter III -- IV The Index and some Plane Topology -- ยง 1 Introduction -- ยง 2 Curves Winding around Points -- ยง 3 Homotopy and the Index -- ยง 4 Existence of Continuous Logarithms -- ยง 5 The Jordan Curve Theorem -- ยง 6 Applications of the Foregoing Technology -- ยง 7 Continuous and Holomorphic Logarithms in Open Sets -- ยง 8 Simple Connectivity for Open Sets -- Notes to Chapter IV -- V Consequences of the Cauchy-Goursat Theoremโ{128}{148}Maximum Principles and the Local Theory -- ยง 1 Goursatโ{128}{153}s Lemma and Cauchyโ{128}{153}s Theorem for Starlike Regions -- ยง 2 Maximum Principles -- ยง 3 The Dirichlet Problem for Disks -- ยง 4 Existence of Power Series Expansions -- ยง 5 Harmonic Majorization -- ยง 6 Uniqueness Theorems -- ยง 7 Local Theory -- Notes to Chapter V -- VI Schwarzโ{128}{153} Lemma and its Many Applications -- ยง 1 Schwarzโ{128}{153} Lemma and the Conformal Automorphisms of Disks -- ยง 2 Many-to-one Maps of Disks onto Disks -- ยง 3 Applications to Half-planes, Strips and Annuli -- ยง 4 The Theorem of CarathSodory, Julia, Wolff, et al -- ยง 5 Subordination -- Notes to Chapter VI -- VII Convergent Sequences of Holomorphic Functions -- ยง 1 Convergence in H(U) -- ยง 2 Applications of the Convergence Theorems; Boundedness Criteria -- ยง 3 Prescribing Zeros -- ยง 4 Elementary Iteration Theory -- Notes to Chapter VII -- VIII Polynomial and Rational Approximationโ{128}{148}Runge Theory -- ยง 1 The Basic Integral Representation Theorem -- ยง 2 Applications to Approximation -- ยง 3 Other Applications of the Integral Representation -- ยง 4 Some Special Kinds of Approximation -- ยง 5 Carlemanโ{128}{153}s Approximation Theorem -- ยง 6 Harmonic Functions in a Half-plane -- Notes to Chapter VIII -- IX The Riemann Mapping Theorem -- ยง 1 Introduction -- ยง 2 The Proof of Caratheodory and Koebe -- ยง 3 Fejer and Rieszโ{128}{153} Proof -- ยง 4 Boundary Behavior for Jordan Regions -- ยง 5 A Few Applications of the Osgood-Taylor-Caratheodory Theorem -- ยง 6 More on Jordan Regions and Boundary Behavior -- ยง 7 Harmonic Functions and the General Dirichlet Problem -- ยง 8 The Dirichlet Problem and the Riemann Mapping Theorem -- Notes to Chapter IX -- X Simple and Double Connectivity -- ยง 1 Simple Connectivity -- ยง 2 Double Connectivity -- Notes to Chapter X -- XI Isolated Singularities -- ยง 1 Laurent Series and Classification of Singularities -- ยง 2 Rational Functions -- ยง 3 Isolated Singularities on the Circle of Convergence -- ยง 4 The Residue Theorem and Some Applications -- ยง 5 Specifying Principal Partsโ{128}{148}Mittag-Lefflerโ{128}{153}s Theorem -- ยง 6 Meromorphic Functions -- ยง 7 Poissonโ{128}{153}s Formula in an Annulus and Isolated Singularities of Harmonic Functions -- Notes to Chapter XI -- XII Omitted Values and Normal Families -- ยง 1 Logarithmic Means and Jensenโ{128}{153}s Inequality -- ยง 2 Mirandaโ{128}{153}s Theorem -- ยง 3 Immediate Applications of Miranda -- ยง4 Normal Families and Juliaโ{128}{153}s Extension of Picardโ{128}{153}s Great Theorem -- ยง 5 Sectorial Limit Theorems -- ยง 6 Applications to Iteration Theory -- ยง 7 Ostrowskiโ{128}{153}s Proof of Schottkyโ{128}{153}s Theorem -- Notes to Chapter XII -- Name Index -- Symbol Index -- Series Summed -- Integrals Evaluated


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram