MATH20101 Complex Analysis Lecture Notes
## MATH20101 Complex Analysis Lecture Notes

### Lecture notes

The lecture notes for the course can be found here:
The lecture notes also contain the exercises and solutions to the
exercises. I will trust you to have a serious attempt at the
exercises *before* referring to the solutions.

There are separate files containing just the exercises here and just the solutions here

*Note to people from outside Manchester*: I understand that
various people outside Manchester have recommended my notes for part
of their Complex Analysis course. If any of you spot any
typos/mistakes/etc in the notes then please let me know (email:
charles dot walkden at manchester dot ac dot uk) - thanks!

### Coursework

The coursework for this course will take the form of a 40 minute
closed-book test held during Week 6 (Reading Week). All questions on
th e test are compulsory and it will be in the format of an exam
question. Thus, looking at past exam papers will provide excellent
preparation for the test. You will need to know sections 2,3,4 from the
course for the test (this is the material that we will cover in weeks
1--5).
A mock coursework test is available here.

### Videos

There are a series of short videos explaining either key points from
the course or commonly-asked questions that are slightly off-topic to
address in lectures. The appropriate time for watching each video is
given in the lecture notes. (Note that these videos are only available
to Manchester students.)
- Argument and modulus in the complex plane
- Why can't we draw the graph of a complex function?
- The Cauchy-Riemann Theorem and its converse
- The complex logarithm and complex powers
- Paths and contours
- Complex integration
- Poles and residues

### Hand-written slides from the lectures

Below will be the visualiser slides from the lectures. My advice would be to read the printed lecture notes above rather than to read the slides; however they may be useful if you want to double-check what I wrote in a lecture.
Week
1,
Week
2 (part 1),
Week
2 (part 2),
Week
3,
Week
4,
Week
5,
Week
7 (part 1),
Week
7 (part 2),
Week
8 (part 1),
Week
8 (part 2),
Week
9,
Week
10,
Week
11,
Week
12 (revision lecture),

### Feedback

You will get feedback on your understanding in this course from (i)
the Week 6 coursework test, (ii) the regular Kahoot! quizzes, (iii)
during the support classes from the PhD demonstrators, (iv) during my
office hour, and (v) via the generic feedback (and exam script
viewing) on the final exam. This feedback will allow you to gauge
your understanding of the material during the course, understand the
mark that you got in the assessment, understand how you could do
better in the future.

### Past exams

Below are the exam papers, together with feedback, for the complex analysis part of the course for the last 3 years.
Tibees,
an Australian Youtuber, has uploaded a video talking about a past exam
for this course. You can watch the
video here