Complex An.·Course
Complex Analysis
Complex analysis: complex numbers, analytic functions, Cauchy integrals, Laurent series, and residues
5
Modules
15
Articles
~2 h
Reading
IV
CLOs
§ 01 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IHolomorphic FunctionsCauchy–Riemann conditions and elementary functions of a complex variable3 articles
18 minBegin → - M IIIntegration in the Complex PlaneCauchy integral, Cauchy’s formula, and Morera’s theorem3 articles
18 minBegin → - M IIILaurent Series and SingularitiesLaurent series expansion, isolated singularities, and their classification3 articles
18 minBegin → - M IVSpecial Methods and FunctionsIntegrals with logarithms, series summation, and special functions3 articles
18 minBegin → - M VEntire Functions and the Laplace TransformWeierstrass theorem, Mittag-Leffler theorem, and applications to ODEs3 articles
18 minBegin →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Analytic Functions
Study analyticity, the Cauchy–Riemann equations, and conformal mappings
CLO II
Integral Theorems
Apply Cauchy’s theorem and the Cauchy integral formula
CLO III
Series and Singularities
Expand functions into Taylor and Laurent series and classify singular points
CLO IV
Residues
Evaluate integrals using the residue method and apply it to physical problems
§ 03 — Practices