### Math 300 - Introduction to Complex Variables.

Syllabus

Getting started with Webwork

Written homeworks:
Assignment #3    Solutions
Assignment #4    Solutions
Assignment #5    Solutions
Assignment #6    Solutions
Assignment #7    Solutions
Assignment #8    Solutions
Assignment #9    Solutions
Assignment #10    Solutions

Midterm #1:   Solutions
Covers Sections 1.1-1.6, 2.1-2.5.
Practice midterm    Solutions
(Our exam covers the same material. This exam was a 1 hour 20 minutes exam during a Tuesday-Thurday class. Our exam will be shorter.)

Midterm #2:    Solutions
Covers Sections 3.1-3.3, 3.5, 4.1-4.6.
Practice midterm    Solutions
The midterm has two problems with pictures missing. The contour in Problem 5 starts with a straight line segment from 0 to 1+2i, then goes along a half-circle with centre 1 and radius 2 from 1+2i to 1-2i, and finally along a straight line back to 0. The contour in problem 7 is a wiggly curve from -i to i, lying on the left half-plane.
Practice problems from textbook

Final Exam:    Tuesday, Dec 15, 3:30-6 PM, BUCH A102
Covers Sections 1.1-1.6, 2.1-2.5, 3.1-3.3, 3.5, 4.1-4.6, 5.1-5.3, 5.5-5.6, 6.1.
Past exams
What is not needed for the final exam:
You don't need to memorize formulas for trigonometric functions and their inverses. These will be provided.You need to know the definitions of various branches of the logarithm, powers, roots. You also need to know the Taylor series of sin(z) and cos(z).
We did not discuss finding harmonic functions with given boundary values, such as Example 2 in Section 2.5. However, you need to know how to find harmonic conjugates as in Example 1 in the same section.
No deformation of curves. It is enough to know the Cauchy's integral theorem: if f(z) is analytic inside and on a simple closed contour, then the integral of f(z) over that contour is zero.
There will be no epsilon-delta proofs in the exam. You need to know how to check the convergence of a series using various tests. There will be no questions about uniform convergence.
Section 5.6 has a list of theorems about the classification of singularities. You need to know how to classify a singularity. This involves computing the Laurent series.
Sections 6.2-6.3 give applications of the residue theorem. We will talk about some of these in class, but they will not be in the exam. The questions in the exam give a function and a closed contour and ask to find the integral.