Welcome

This course introduces the calculus of complex functions of a complex variable. It turns out that complex differentiability is a very strong condition and differentiable functions behave very well. Integration is along paths in the complex plane. The central result of this spectacularly beautiful part of mathematics is Cauchy's Theorem guaranteeing that certain integrals along closed paths are zero. This striking result leads to useful techniques for evaluating real integrals based on the 'calculus of residues'.

If you have any questions please do not hesitate in contacting me:

• Dr Charles Walkden
• charles.walkden@manchester.ac.uk
• Alan Turing Building, 2.241

Where to find course information

On the Course Information page you will find important information about this course including: course learning outcomes and details of the course syllabus. In addition you will want to read Succeeding in this Course Unit, also in the Course Information section.

Your course assessment information will appear on the Assessment & Feedback page where you will also find details here of what feedback you will receive during the course, when you will receive it and how it can help in your future assessment tasks.

Course materials and resources can be found below.

Lecture notes & Exercises and Solutions

A preliminary version of the lecture notes for the course can be found here:

• Lecture notes (which also contain the exercises and solutions) (preliminary version)
• Just the exercises.
• Solutions to the exercises.

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.

Hand-written slides from the lectures

Below are 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, Week 3, Week 4, Week 4 tutorial work, Week 5, Week 5 tutorial work, Week 6, Week 6 tutorial work, Week 7 revision lecture, Week 8, Week 9, Week 10, Week 11, Week 12 (revision lectures).

Lecture podcasts can be accessed from https://video.manchester.ac.uk/lectures (requires sign in).