A Friendly Approach to Complex Analysis

Contents
Overview
	What is complex analysis?
	Why study complex analysis?
Chapter 1. Complex numbers and their geometry
	1.1. The field of complex numbers
	1.2. Geometric representation of complex numbers
	1.3. Topology of C
	1.4. The exponential function and kith
Chapter 2. Complex differentiability
	2.1. Complex differentiability
	2.2. Cauchy-Riemann equations
	2.3. Geometric meaning of the complex derivative
Chapter 3. Cauchy Integral Theorem
	3.1. Definition of the contour integral
	3.2. Properties of the contour integral
	3.3. Fundamental Theorem of Contour Integration
	3.4. The Cauchy Integral Theorem
	3.5. Existence of a primitive
	3.6. The Cauchy Integral Formula
	3.7. Holomorphic functions are infinitely complex differentiable
	3.8. Liouville’s Theorem, Fundamental Theorem of Algebra
	3.9. Morera’s Theorem
	3.10. Appendix
Chapter 4. Taylor and Laurent series
	4.1. Series
	4.2. Power series
	4.3. Taylor series
	4.4. Classification of zeroes
	4.5. The Identity Theorem
	4.6. The Maximum Modulus Theorem
	4.7. Laurent series
	4.8. Classification of singularities
	4.9. Residue Theorem
Chapter 5. Harmonic functions
	5.1. What is a harmonic function?
	5.2. Link between harmonic and holomorphic functions
	5.3. Consequences of the two way traffic
Solutions
	Solutions to the exercises from the Introduction
	Solutions to the exercises from Chapter 1
	Solutions to the exercises from Chapter 2
	Solutions to the exercises from Chapter 3
	Solutions to the exercises from Chapter 4
	Solutions to the exercises from Chapter 5
Some real analysis background
Notes
Bibliography
Index