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Complex Analysis
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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
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