Complex Analysis, Spring 2017

Wed 5/17: Final Oral Exam questions.

Final Exam Questions

Tue 5/16: Moduli space of lattices; modular forms.

Thu 5/11: Addition formula for an elliptic curve.

Tue 5/9: Theta function and functional equation for Riemann zeta.

Thu 5/4: Fourier inversion, Poisson Summation.

Thu 4/27: Field of elliptic functions, the torus as an elliptic curve.

Tue 4/25: Weierstrass P-function.

Thu 4/20: Elliptic functions.

Wed 4/19: Homework 6.

Due on Thursday 4/27.

Tue 4/18: Weierstrass products, Mittag-Leffler theorem.

Thu 4/13: The Gamma function continued.

Tue 4/11: The Gamma function.

Thu 4/6: Homework 5.

Due on Thursday 4/13.

Thu 4/6: Residue Theorem continued.

Tue 4/4: Residue Theorem.

Tue 3/21: Meromorphic functions.

Thu 3/16: Laurent decompositions and series.

Tue 3/14: Singularities of analytic functions.

Thu 3/9: Homework 4.

Due on Thursday 3/16.

Thu 3/9: Analytic continuation.

Tue 3/7: Power series.

Thu 3/2: Morera’s Theorem; sequences and series of functions.

Wed 3/1: Homework 3.

Due on Thursday 3/9.

Tue 2/28: Cauchy’s Integral formulas.

Thu 2/23: Cauchy’s Theorem.

Tue 2/21: Homework 2.

Due on Tuesday 02/28.

Tue 2/21: Complex line integrals.

Thu 2/16: Complex differentiability continued.

Tue 2/14: Complex differentiability.

Thu 2/9: Complex exponential, trig functions and logarithms. Review of topological concepts..

Wed 2/8: Homework 1.

Due on Thursday 02/16.

Tue 2/7: Complex numbers, sequences and series.