MP2 · Complex analysis
A 26-module path through mp2 · complex analysis, in study order from foundations to the frontier.
Modules
- Complex Numbers and the Complex Plane
- Functions of a Complex Variable and Limits
- Analytic Functions and the Cauchy-Riemann Equations
- Harmonic Functions and Conjugates
- Elementary Complex Functions
- Complex Integration and Contour Integrals
- Cauchy's Integral Theorem
- Cauchy's Integral Formula and Derivatives
- Consequences: Liouville, Maximum Modulus, Morera
- Taylor Series of Analytic Functions
- Laurent Series
- Zeros, Poles, and Isolated Singularities
- Residues and the Residue Theorem
- Evaluation of Real Integrals by Contour Methods
- Argument Principle and Rouche's Theorem
- Branch Points, Branch Cuts, and Riemann Surfaces
- The Point at Infinity and the Riemann Sphere
- Conformal Mapping
- Mobius Transformations
- Riemann Mapping Theorem and Schwarz-Christoffel
- Applications to Potential and Fluid Flow
- Analytic Continuation
- Schwarz Reflection Principle
- Dispersion Relations and Kramers-Kronig
- Saddle-Point and Steepest-Descent Methods
- Analytic Structure of Singular Integrals