MATH 411 - Honors Complex Variables

3 units (fi 6)(FIRST, 3-0-0)

Faculty of Science

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; calculus of residues, argument principle, and Rouche's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as: Normal families, The Riemann mapping Theorem, Picard's Theorem. Prerequisite: MATH 314 or 317. Notes: (1) This course is primarily for Honors students in Mathematics or Physics. (2) Offered in alternate years. It may be offered in intervening years if demand is sufficient.