Description



Table of Contents
Prerequisites and Preliminaries.- Curves, Connectedness and Convexity.- (Complex) Derivative and (Curvilinear) Integrals.- Power Series and the Exponential Function.- The Index and some Plane Topology.-Consequences of the Cauchy–Goursat Theorem—Maximum Principles and the Local Theory.- Schwarz' Lemma and its Many Applications.- Convergent Sequences of Holomorphic Functions.- Polynomial and Rational Approximation—Runge Theory.- The Riemann Mapping Theorem.- Simple and Double Connectivity.- Isolated Singularities.- Omitted Values and Normal Families.- Bibliography.- Name Index.- Subject Index.- Symbol Index.- Index of Series Summed and Integrals Evaluated.

Classical Analysis in the Complex Plane

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A Hardback by Robert B. Burckel

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    View other formats and editions of Classical Analysis in the Complex Plane by Robert B. Burckel

    Publisher: Birkhäuser
    Publication Date: 10/12/2021 12:00:00 AM
    ISBN13: 9781071619636, 978-1071619636
    ISBN10: 1071619632
    Also in:
    Complex analysis, complex variables

    Description



    Table of Contents
    Prerequisites and Preliminaries.- Curves, Connectedness and Convexity.- (Complex) Derivative and (Curvilinear) Integrals.- Power Series and the Exponential Function.- The Index and some Plane Topology.-Consequences of the Cauchy–Goursat Theorem—Maximum Principles and the Local Theory.- Schwarz' Lemma and its Many Applications.- Convergent Sequences of Holomorphic Functions.- Polynomial and Rational Approximation—Runge Theory.- The Riemann Mapping Theorem.- Simple and Double Connectivity.- Isolated Singularities.- Omitted Values and Normal Families.- Bibliography.- Name Index.- Subject Index.- Symbol Index.- Index of Series Summed and Integrals Evaluated.

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