Introduction to Complex Analysis
by W W L Chen
Publisher: Macquarie University 2003
Number of pages: 194
A set of notes suitable for an introduction to some of the basic ideas in complex analysis: complex numbers; foundations of complex analysis; complex differentiation; complex integrals; Cauchy's integral theorem; Cauchy's integral formula; Taylor series, uniqueness and the maximum principle; isolated singularities and Laurent series; Cauchy's integral theorem revisited; residue theory; evaluation of definite integrals; harmonic functions and conformal mappings; Möbius transformations; Schwarz-Christoffel transformations; uniform convergence.
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by Heinrich Burkhardt - D. C. Heath
Contents: Complex numbers and their geometrical representation; Rational functions of a complex variable; Theory of real variables and their functions; Single-valued analytic functions of a complex variable; General theory of functions; etc.
by Leif Mejlbro - BookBoon
This is an introductory book on complex functions theory. From the table of contents: Introduction; The Complex Numbers; Basic Topology and Complex Functions; Analytic Functions; Some elementary analytic functions; Index.
by Christian Berg - Kobenhavns Universitet
Contents: Holomorphic functions; Contour integrals and primitives; The theorems of Cauchy; Applications of Cauchy's integral formula; Zeros and isolated singularities; The calculus of residues; The maximum modulus principle; Moebius transformations.
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This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the case of rational maps of the Riemann sphere. The book introduces some key ideas in the field, and forms a basis for further study.