Math 411: Complex Variables I
Fall, 2011        Dr. John Bowman

The complex number system. Analytic functions. Cauchy's integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications: the calculus of residues, the argument principle, and Rouché's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as normal families, the Riemann mapping theorem, and Picard's theorem.

John Bowman 2011-10-04