PHYS 20672 Complex Variables and Vector Spaces
- Textbooks: I
et al Complex Variables (in the Schaum's
Arfken & Weber Mathematical Methods for
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
- The last examples class was
at 10.00 on Monday 13 May in the Braddick Library
rooms L1-L3, Floor 1 Schuster Building.
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):
- Scans of the visualizer slides are available on Blackboard.
online tool to help with visualizing conformal mappings. From
the same source you might also
map projections. Note that when you have one shape-preserving
mapping from the sphere to the x,y plane
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:
My view on maths examples is that it is better to get more practice
rather than less. However, some questions intended partly to extend
your understanding have been marked with one or two dieses (‡
or ‡‡). In the early sheets these are not usually
harder than other problems, but you may want to give them lower
priority. Problems marked with an asterisk (*) are not intended to
be lower priority, but they may be more challenging; I recommend
that you try them, but set yourself a time limit.
- 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
- For practice on short past exam questions on vector spaces, see
For practice on longer questions (and for a wider variety of short
questions) you should study examples sheets 6 and 7 (but not
questions or parts of questions marked with a diesis,
- 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),(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
- Please let me
know if you find errors in the summaries and examples