This course is core for Physics with Theoretical Physics students. It should be taken by other mathematically able students who are interested in theoretical physics; it is useful for a variety of courses in 3rd and 4th year, particularly quantum field theory, and is "desirable but not essential" for Mathematical Methods for Physicists (PHYS30672)

The Blue Book entry for this course is here. The primary recommended textbooks for most of the course is "Complex Variables", M. R. Spiegel et al. (Schaum's outlines). This very useful textbook is available as an ebook. You will need to log on to Dawsonera with your UoM central user name and password (select "shibboleth login", and then "Unversity of Manchester" from the drop-down list; after that return to this link which will take you directly to the book). References are also given to the three "Mathematical Methods" books Arfken, Riley and Boas, one of which you probably already own. (The first two are available as ebooks, which can also be accessed via the "reading list" link on the Blackboard page for this course.) You will find these increasingly useful as the course goes on; in general, Spiegel is good for the foundations and the "Mathematical Methods" books are good for applications, and for integral transforms which are not covered by Spiegel.

Links to "HELM" self-study material covering much of the course are here.

The lectures for the course are on Mondays at 3-4pm and Thursday at at 10am, both in Blackett.

There will also be examples classes at 4pm on alternate Mondays in the Braddick library (Schuster, 1st floor) starting on the 8th Feb. These will be "workshop-style", not "lecture style": you should attempt the sheet in advance, and use the examples class to sort out problems in groups with guidance from demonstrators when required. Work may be handed in for marking at the subsequent Thursday lecture, and the solutions will be posted on the same day.

All the past papers from 2010 onwards were written by the current lecturer and so provide a good guide to the style of this year's exam. They are available, along with bottom-line answers and comments, in the UG virtual common room on Blackboard.

I have noticed that the references to Riley in the summaries below do not correspond to the ebook, third, edition, but to edition 1 (1996) of the 3-author version. I will updated them when I have time; the materials of the complex variables part of the course are now in chapters 24 and 25.

There will be no lecture on the 12th May. When revising, please note that I will not be avaiable from the 3rd June until the exam. Before that the Physics Help Service will run on the dates shown here.If you experience problems with the following pages, please check that your browser is MathJax compatible.

- Lecture 1: Complex numbers
- Lecture 2: Functions of complex numbers, Functions as mappings
- Lecture 3, 4: Differentiation and the Cauchy-Riemann equations
- Lecture 5, 6: Conformal mappings
- Lecture 7: Integration in the complex plane
- Lecture 8: Cauchy's theorem
- Lecture 9, 10: Cauchy's integral formulae
- Lecture 11-13: Taylor and Laurent Series
- Lecture 14-16: Residue Theorem; Real Integrals
- Lecture 17,18: Integral Transforms; Fourier Transforms
- Lecture 19-21: Laplace Transforms
- Lecture 22: Overview of course and testable skills

- Examples 1
- Solutions 1 (22/3/16: typos in 2a) and 7d) corrected)
- Examples 2
- Solutions 2
- Examples 3
- Solutions 3
- Examples 4
- Solutions 4
- Examples 5 (26/4/16: Start of question 37 reworded for greater clarity)
- Solutions 5
- Examples 6
- Solutions 6

- Handout 1
- Equipotentials and field lines
- Finding residues
- Diagrams for lecture 18: delta series and convolution
- Table of Laplace Transforms