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 Leicester (and others): I understand that Jeremy Levesley has recommended my notes for part of the Complex Analysis course at Leicester. 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!


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.


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.
  1. Argument and modulus in the complex plane
  2. Why can't we draw the graph of a complex function?
  3. The Cauchy-Riemann Theorem and its converse
  4. The complex logarithm and complex powers
  5. Paths and contours
  6. Complex integration
  7. 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),


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.