Complex Analysis

Por: Swayam . en: ,

Week 1: Algebra and Topology of the complex plane
Week 2:Geometry of the complex plane, Complex differentiation
Week 3: Power series and its convergence, Cauchy-Riemann equations
Week 4: Harmonic functions,Möbius transformations
Week 5:Integration along a contour, The fundamental theorem of calculus
Week 6: Homotopy, Cauchy’s theorem
Week 7: Cauchy integral formula, Cauchy’s inequalities and other consequences
Week 8: Winding number, Open mapping theorem, Schwarz reflection Principle
Week 9: Singularities of a holomorphic function, Laurent series
Week 10: The residue theorem, Argument principle, Rouche’s theorem
Week 11: Branch of the Complex logarithm, Automorphisms of the Unit disk
Week 12: Covering spaces, Picard's theorem