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Course Material for Metric Spaces and Complex Analysis
This lecture note begins by introducing students to the language of topology before using it in the exposition of the theory of (holomorphic) functions of a complex variable. The central aim of the lecture note is to present Cauchy's Theorem and its consequences, particularly series expansions of holomorphic functions, the calculus of residues and its applications.
Author(s): University of Oxford
NA Pages 
Introduction to Complex Analysis by George Voutsadakis
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
67 Pages
This note explains the following topics: Complex differentiation, Contour integration and residue calculus.
Author(s): I Smith
71 Pages
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
294 Pages
Complex Analysis Lecture notes by Nikolai Dokuchaev
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.
Author(s): Nikolai Dokuchaev, Trent University
58 Pages
Introduction to Complex Analysis by Michael Taylor
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.
Author(s): Michael Taylor
478 Pages
Introduction to Complex Analysis excerpts by B.V. Shabat
This note covers the following topics: The Holomorphic Functions, Functions Of A Complex Variable, Properties Of Holomorphic Functions, The Basics Of The Geometric Theory, The Taylor Series.
Author(s): B.V. Shabat
111 Pages
Complex Analysis by Christer Bennewitz
This note explains the following topics: Complex functions, Analytic functions, Integration, Singularities, Harmonic functions, Entire functions, The Riemann mapping theorem and The Gamma function.
Author(s): Christer Bennewitz
116 Pages
Complex Analysis Lecture Notes by Dan Romik
This note covers the following topics: The fundamental theorem of algebra, Analyticity, Power series, Contour integrals , Cauchy’s theorem, Consequences of Cauchy’s theorem, Zeros, poles, and the residue theorem, Meromorphic functions and the Riemann sphere, The argument principle, Applications of Rouche’s theorem, Simply-connected regions and Cauchy’s theorem, The logarithm function, The Euler gamma function, The Riemann zeta function, The prime number theorem and Introduction to asymptotic analysis.
Author(s): Dan Romik
129 Pages