Complex Analysis
A 24-module path through complex analysis, in study order from foundations to the frontier.
Modules
- Complex Numbers and the Complex Plane
- Complex Functions and Limits
- The Cauchy-Riemann Equations
- Holomorphic Functions
- Harmonic Functions and Holomorphy
- The Complex Exponential and Logarithm
- Contour Integrals
- The ML Inequality and Estimates
- Cauchy's Theorem
- Antiderivatives and Path Independence
- Cauchy's Integral Formula
- Power Series and Analyticity
- Taylor Series of Holomorphic Functions
- The Identity Theorem and Zeros
- Liouville's Theorem and Applications
- Laurent Series
- Singularities and Classification
- The Residue Theorem
- Evaluation of Real Integrals
- The Argument Principle and Rouche's Theorem
- The Maximum Modulus Principle
- Conformal Mappings
- Mobius Transformations
- Analytic Continuation