Math 6311 Complex analysis
Complex analysis is a branch of mathematics investigating functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering. This course will cover:
- Preliminaries to complex analysis; Complex differentation and integration; Cauchy’s integral theorem and formula; Taylor’s series and maximum principle; Isolated singularities and Laurent series; Evaluation of residues and integrals; Harmonic functions and conformal mappings; MoÌˆbius and Schwarz-Christoffel transformations; Applications to fluid dynamics.
Good courses in advanced calculus and real analysis.
- Theory of complex functions by Reinhold Remmert, Springer, 1991.
- Classical topics in complex function theory by Reinhold Remmert, Leslie Kay, Springer, 2010.