are four problem sets for this course:
Pdf slides for the revision lectures can be found here.
Much of the background
for set 1 has been covered in year 1 and the main purpose of
this set is to focus in on the specific issues relevant for
this course. There should be no problem setting this early on
in term - students will be able to read up on the one or two
new ideas required. The material required for sets 2, 3 and 4
should be covered by the end of weeks 3, 5 and 7,
Many questions on the
problems sets have been taken over from John Magorrian and his
old problem sheets and excellent lecture notes can be found here.
This year, the problem sheets also have additional computational
problems. Computational methods, both numerical and symbolic,
are of increasing importance in physics and symbolic
computational tools have become significantly more powerful over
the past decade or so. This is changing the way physicists work.
Much as the introduction of the pocket calculator some 50 years
ago has made by-hand numerical calculations unnecessary, modern
systems such as Mathematica, can now take over standard symbolic
calculations, such as algebraic manipulations or integration.
This facilitates powerful checks of by-hand calculations but
also allows for calculations which are virtually intractable
with a pen-and-paper approach.The following problems present an
opportunity to practice some of these methods in the context of
topics from the Mathematical Methods course. They are
supplementary and voluntary but strongly recommended and
hopefully a fun way to engage with symbolic computations early
on. The problems are meant for realisation in Mathematica which
can be downloaded from the university server. Mathematica is
easy to use, has good built-in documentation and many high-level
mathematical functions - you can start to experiment