TABLE OF CONTENTS

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PREAMBLE

• Introduction
• License
• Acknowledgements
• Reader's Comments

CHAPTER 1

• A Brief History
• Terminology and Notation
• Geometric Interpretation
• The Principal Argument
• Roots of Complex Numbers
• Topology of the Complex Plane

CHAPTER 2

• Complex Functions
• Riemann Sphere
• Complex Differentiation
• The Logarithmic Function
• Riemann surfaces: Examples

CHAPTER 3

• Mappings
• The Transformation 1/z
• Analytic Landscapes
• Domain Coloring
• The Complex Power Function

CHAPTER 4

• Curves in the Complex Plane
• Complex Integration
• Integrals of Functions with Branch Cuts

CHAPTER 5

• Series
• Taylor Series
• Laurent Series
• Classification of Singularities
• The Mandelbrot Set
• The Julia Set

CHAPTER 6

• Applications of Conformal Mappings
• Complex Potential: Basic examples
• Uniform Flow Around a Circle
• Joukowsky Airfoil

FURTHER READING

• Bibliography