MA205: Complex Analysis

This is an introductory course in Complex Analysis for undergraduates in their sophomore year.

I was a TA for the Autumn 2021 offering of this course under Professor Sudarshan Gurjar. The course covers the following.

• Holomorphic and analytic functions.
• Cauchy-Riemann equations and harmonic functions.
• Power series and their convergence via the root test and ratio test.
• The exponential, sine, and cosine functions.
• Zeroes and poles of analytic functions.
• Cauchy’s Theorem and Cauchy’s Integral Formula.
• The complex logarithm and singularities.
• Laurent Series and Cauchy’s Residue Theorem.
• Evaluating Real Integrals via Cauchy’s Residue Theorem.
• Some exotic results including but not limited to Liouville’s Theorem, Casorati-Weierstrass Theorem, Argument Principle, Rouché’s Theorem, the Little and Big Picard Theorems.
• Conformal mappings.

My solutions for the tutorial problems can be viewed here