Complex Analysis
Calculus & Analysis
Master the elegant theory of functions of a complex variable: analytic functions, Cauchy's theorem, residues, conformal mappings, and analytic continuation.
Learning Objectives
- Work fluently with complex numbers in Cartesian and polar form
- Apply the Cauchy-Riemann equations to identify analytic functions
- Use Cauchy's integral formula and the residue theorem
- Expand functions in Laurent series and classify singularities
- Evaluate real integrals using contour integration
- Understand conformal mappings and the Riemann mapping theorem
Lessons
1
Complex Numbers & the Complex Plane
35 min
2
Analytic Functions & the Cauchy-Riemann Equations
35 min
3
Cauchy's Integral Theorem & Formula
35 min
4
Laurent Series & Singularities
35 min
5
The Residue Theorem & Real Integral Evaluation
35 min
6
Conformal Mappings
35 min
7
The Gamma Function & Analytic Continuation
35 min
Quick Practice
Test your knowledge with a quick interactive challenge from this module.
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Key Concept Flashcards
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