Course Details
Subject {L-T-P / C} : MA6103 : Advanced Complex Analysis { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Shesadev Pradhan
Syllabus
Spherical representation of extended complex plane, Analytic functions, Branches of multiple-valued functions, Cauchy’s theorem, Singularities, Argument principle, Calculus of residues, Harmonic functions, Poisson’s formula, reflection principle, Conformal mappings, Geometry of Mobius transformations, Open mapping theorem, Maximum modulus theorem, Schwarz’s lemma, Partial fractions and factorization, Stirling’s formula, Jensen’s formula, Hadamard’s theorem, Little and Great Picard Theorem.
Course Objectives
- NA
- NA
Course Outcomes
NA
Essential Reading
- J. B. Conway, Functions of One Complex Variable, Springer, 1978.
- L. V. Ahlfors, Complex Analysis,, Mc-Graw Hill International, 1979
Supplementary Reading
- W. Rudin, Real and Complex Analysis, McGraw-Hill, 1986.
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