# Table of Contents

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### Preamble

### 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
- Limits
- Riemann Sphere
- Continuity
- Complex Differentiation
- The Logarithmic Function
- Riemann surfaces: Examples

### Chapter 3

### Chapter 4

### 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