Mathematical Methods

Prof Andre Lukas

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, respectively. 

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 immediately.