- Textbooks: I
recommend Spiegel
et al
*Complex Variables*(in the*Schaum's outlines*series), Arfken & Weber*Mathematical Methods for Physicists*or Riley, Hobson & Bence*Mathematical Methods for Physics and Engineering*. For much of the material on vector spaces of finite dimension, Riley is a useful reference. The first chapter of R. Shankar,*Principles of Quantum Mechanics*, may be more generally useful; it can be found on Blackboard.

- The last examples class was
at
**10.00 on Monday 13 May**in the**Braddick Library rooms L1-L3**, Floor 1 Schuster Building. In the run-up to the exams, it should usually be possible to find me in my office (7.17 Schuster Building).

- Lecture summaries (for lectures 1-16, refs to Riley refer to the
first edition, not the third edition available online -- will be
corrected in time):
- Lectures 1-4
- Lectures 5-7
- Lectures 8-12
- Lectures 13-16
- Lectures 17-21 (from this point onwards, "Riley" refers to the third edition, available online)
- Lectures 22-23

- Scans of the visualizer slides are available on Blackboard.

- Downloads:
- Mappings of the complex plane defined by some simple functions.
- An illustration of the argument theorem.
- Solutions of Laplace's equation obtained by conformal mapping.

- An
online tool to help with visualizing conformal mappings. From
the same source you might also
like world
map projections. Note that when you have one shape-preserving
mapping from the sphere to the x,y plane
(e.g., Mercator's
projection), you can obtain many others by conformal mapping.
So if you like maps, this could be an
__important__application of functions of a complex variable!

- Examples sheets and worked solutions:
- Examples 1 and Solutions 1 (released 2019)
- Examples 2 and Solutions 2 (released 2019)
- Examples 3 and Solutions 3 (released 2019)
- Examples 4 and Solutions 4 (released 2019)
- Examples 5 and Solutions 5 (released 2019, solutions to Q.42 clarified 13.05.2019)
- Examples 6, Solutions 6, Part 1 and Solutions 6, Part 2 (released 2019)
- Examples 7 and Solutions 7 (released 2019)

- The format of the exam is similar to previous years' papers for
PHYS20672:
**one**compulsory question (consisting of several short questions covering the whole course) and a choice of**two out of three**longer questions. Two of the longer questions will be on complex variables and one will be on vector spaces.

- For practice on short past exam questions on vector spaces, see
- PHYS30201: 2016/17 1(a); 2015/16 1(b); 2014/15 1(a),(b),(d);
2013/14 1(a) [1(e) should also be OK, with the understanding
that
*x*is position and that momentum*p*is related to*k*by a factor of ℏ). - PHYS20602: 2011/12 1(a),(d)(i),(d)(ii); 2010/11 1(a),(b),(d); 2009/10 1(a); 2008/09 1(a). [Local copies are provided in the two cases where it's painful to extract the papers from Blackboard -- the problem may have been fixed by now.]

- PHYS30201: 2016/17 1(a); 2015/16 1(b); 2014/15 1(a),(b),(d);
2013/14 1(a) [1(e) should also be OK, with the understanding
that

- Please let me know if you find errors in the summaries and examples sheets/solutions.