Math 185: Complex Analysis
Lecture 3, Fall 2014

Course Information

The official course description from the catalog is: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

We will study the additional structure provided by complex differentiation. While some parts of complex analysis will look familiar from real analysis, we will quickly find that in many ways, complex analysis is more rigid. This will allow us to compute things like integrals by studying functions just at specific points, without having to do the hard work of finding anti-derivatives.

Along the way, we will study other nice properties of complex analytic functions, such as the maximum principle, Liouville's theorem, and conformalness.

Classroom

This course meets MWF 11am-12pm in 4 Evans.

Miscellaneous

The solutions for the final exam have been posted.

Some suggested exercises, if you would like some practice on Fourier series: Exercise VI.5.2, Exercise VI.6.1, Exercise VI.6.3.

The formula sheet that will be on the final exam has been posted.

There are notes on the Fourier transform from the final lectures on Friday.

The spring 2014 final and solutions have been posted. Please ignore 2(d) and 2(f), as those are related to the prime number theorem, which we did not cover.

The due date for Homework #7 has been changed to Friday, November 14 at the beginning of class. Homeworks will need to be turned in within the first five minutes of class, or must be in my office prior to 10:45am. There will be no office hours on Monday, November 10 and Wednesday, November 12.

Midterm 2 was in class on October 31. Solutions have been posted.

The spring 2014 midterm 2 and solutions are available.

Midterm 1 was in class on September 29. Solutions have been posted.

The spring 2014 midterm 1 and solutions are available.

The course website for the Spring 2014 version of this course is also available.