Theory of Complex Variables: Course Outline (MAT-604)

• Harmonic functions.
• The Riemann mapping theorem.
• Conformal mappings  for multi-connected domains.
• Elliptic functions and Picard's theorem.
• Analytic continuation. Entire functions.
• Range of an analytic function.
• Topics in univalent functions and geometric functions theory.
• Phargmen-Lindelof theorem.
• Zeros of analytical functions. 
• Jensen’s formula. 
• Weirestrass factorization theorem.

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