Lectures
Mondays, Tuesdays, Thursdays 11:00 AM -12:00 PM
Tutorials
Alternate Thursdays 11:00 AM - 12:00 PM
Weekly homework problems will be uploaded here.
Office Hour
Thursdays 5:00-6:00 PM
Course Contents
Derivative of a function of several variables, Inverse function theorem, Implicit function theorem.
Holomorphic functions, The local Cauchy theorem, Power series representation, Zeros and singularities, The open mapping theorem, The global Cauchy theorem, The calculus of residues.
Schwarz lemma, the automorphisms of the disc and the upper half plane, Conformal mappings, Riemann mapping theorem
Runge's theorem, Mittag-Leffler theorem, Simply connected regions.
Optional topics: Harmonic functions, The Phragmen-Lindelöf method, Wierstrass factorization, Analytic continuation, Elliptic functions
References
Multivariable Differential Calculus
1. T. Apostol, Mathematical Analysis
2. S. Kumaresan, A Course in Differential Geometry and Lie Groups
3. M. Spivak, Calculus on Manifolds
Complex Analysis
1. L. V. Ahlfors, Complex Analysis
2. J. B. Conway, Functions of one complex variable
3. R. Remmert, Theory of complex functions
4. Walter Rudin, Real and Complex Analysis
5. E. M. Stein and Rami Shakarchi, Complex Analysis
Evaluation
End-sem 35%
Mid-sem 35%
Quizzes 20%.
Presentation 10%