### 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.