The contents of this
book include: Complex numbers, Polynomials and rational functions, Riemann
surfaces and holomorphic maps, Fractional linear transformations, Power series,
More Series, Exponential and trigonometric functions, Arcs, curves, etc, Inverse
functions and their derivatives, Line integrals, Cauchy’s theorem, The winding
number and Cauchy’s integral formula, Higher derivatives, including Liouville’s
theorem, Removable singularities, Taylor’s theorem, zeros and poles, Analysis of
isolated singularities, Local mapping properties, Maximum principle, Schwarz
lemma, and conformal mappings, Weierstrass’ theorem and Taylor series, Plane
topology, The general form of Cauchy’s theorem, Residues, Schwarz reflection
principle, Normal families, Arzela-Ascoli, Riemann mapping theorem, Analytic
continuation, Universal covers and the little Picard theorem.

This note explains the following topics: Complex
Numbers and Their Properties, Complex Plane, Polar Form of Complex Numbers,
Powers and Roots, Sets of Points in the Complex Plane and Applications.

Author(s): George Voutsadakis,Lake Superior State University

This PDF covers the following topics related to Complex
Analysis : The Real Field, The Complex Field, Properties of holomorphic
functions, The Riemann Mapping Theorem, Contour integrals and the Prime
Number Theorem, The Poisson representation, Extending Riemann maps.

Author(s): Eric T. Sawyer, McMaster University,
Hamilton, Ontario

The contents of this
book include: Complex numbers, Polynomials and rational functions, Riemann
surfaces and holomorphic maps, Fractional linear transformations, Power series,
More Series, Exponential and trigonometric functions, Arcs, curves, etc, Inverse
functions and their derivatives, Line integrals, Cauchy’s theorem, The winding
number and Cauchy’s integral formula, Higher derivatives, including Liouville’s
theorem, Removable singularities, Taylor’s theorem, zeros and poles, Analysis of
isolated singularities, Local mapping properties, Maximum principle, Schwarz
lemma, and conformal mappings, Weierstrass’ theorem and Taylor series, Plane
topology, The general form of Cauchy’s theorem, Residues, Schwarz reflection
principle, Normal families, Arzela-Ascoli, Riemann mapping theorem, Analytic
continuation, Universal covers and the little Picard theorem.

This book explains the following topics: Introduction to Complex Number
System, Sequences of Complex Numbers, Series of Complex Number,
Differentiability, Complex Logarithm, Analytic Functions, Complex Integration,
Cauchy Theorem, Theorems in Complex Analysis, Maximum and Minimum Modulus
principle, Singularities, Residue Calculus and Meromorphic Functions, Mobius
Transformation.

Author(s): Institute of Distance and Open Learning, University of
Mumbai

The contents of this book include: Complex numbers, Elements of
analysis, Complex integration: path integrals,Laurent series, Winding numbers,
Transforms for representation of processes in frequency domain.

In this note
the student will learn that all the basic functions that arise in calculus,
first derived as functions of a real variable, such as powers and fractional
powers, exponentials and logs, trigonometric functions and their inverses, and
also many new functions that the student will meet, are naturally defined for
complex arguments.

This note
explains the following topics: Complex functions, Analytic functions,
Integration, Singularities, Harmonic functions, Entire functions, The
Riemann mapping theorem and The Gamma function.