MT2C06TM25 – Complex Analysis
1: Explain the fundamental concepts of complex analysis, including the Riemann Sphere, stereographic projections, power series, conformal mappings, and linear transformations.
2: Apply Cauchy integral theorem and formula to evaluate complex integrals, utilizing concepts like line integrals, Cauchy’s theorem in various regions, and the index of a point with respect to a closed curve.
3: Interpret the fundamental theorems in Complex Analysis, such as Morera’s Theorem, Liouville’s Theorem, and Cauchy’s Estimate, to solve problems involving analyticity, singularities, and maximum principles.
4: Solve complex analysis problems using the calculus of residues, including evaluating
definite integrals and applying the residue theorem and the argument principle in multiply
connected regions.
- Teacher: josmy thomas