Course Content

• In the second semester we hope to cover many of the classical and important results in the theory of complex variables. These include the Mittag-Leffler Theorem, Weierstrass factorization, Schwarz reflection principle, analytic continuation, harmonic and subharmonic functions, the Dirichlet problem in simply connected domains, Riemann surfaces, the gamma function, Riemann’s zeta function and the prime number theorem, Runge’s theorem the Schwarz-Christoffel formula, Phragmen-Lindelof, Hadamard’s three circle theorem, Picard’s bit theorem, Jensen’s theorem, doubly periodic functions and the Weierstrass theory. If time permits we will study linear differential equations in the complex plane. Some References

Some References