This is the non-bcourses version of the webpage for Math 185, lecture 2, as offered in Spring 2026. Note that although some materials may be common to other versions of the class, e.g. my Fall 2025 section, others will not be, and policies may differ.
The syllabus can be found here. Lecture notes, homework, and other materials can be found below.
Instructor: Avi Zeff
Time/place: Monday, Wednesday, and Friday 3-4 PM, in Etcheverry 3111
Office hours: Wednesday 11 AM - 1 PM and Friday 11 AM - 12 PM in 860 Evans Hall
Lecture 1: introduction, complex numbers and representations
Lecture 2: stereographic projection and first branch cuts
Lecture 3: the logarithm and power functions
Lecture 4: trigonometric functions and notions from analysis
Lecture 5: the Cauchy-Riemann equations
Lecture 7: the Poisson integral formula
Lecture 9: complex line integrals
Lecture 10: using Cauchy's formula
Lecture 11: applications of Cauchy's formula to analyticity
(Lecture 13 was cancelled, and the numbering maintained to better align with last semester's numbering)
Lecture 14: series and convergence
Lecture 17: series expansions at infinity and other properties
Lecture 18: analytic continuation
Lecture 19: Laurent expansions
Lecture 20: isolated singularities
Lecture 21: the residue theorem
Lecture 22: applications of the residue theorem
Lecture 23: the argument principle
Lecture 24: the open mapping principle
Lecture 25: a taste of (co)homology
Further practice problems on power series, Laurent series and the residue theorem, all topics
Project guidelines