Aims and Objectives
This module builds upon the first year Maths and Computing module, and introduces the essential mathematics required for the remaining level 5, 6 and 7 physics modules. In particular, the module covers those mathematical methods that are essential for an understanding of quantum mechanics, electromagnetism, condensed matter and optics.
At the end of the module, students should be able to:
Solve a range of Partial Differential Equations (PDEs) using standard techniques.
Calculate Fourier Series and Fourier Transforms of functions.
Use integral theorems such as Stokes theorem, Gauss theorem to simplify and solve problems using vector calculus.
Solve problems on the above topics using computational methods.
An indicative list of topics covered by this module, but which may change slightly from year to year, is given by:
Introduction to the Delta function and Gaussian integrals;
Definition and calculation of Fourier Series and Fourier Transforms;
Introduction to Curvilinear co-ords: how to specify, base vectors, grad/div/curl;
Introduction and solution of PDE's (wave equation, heat transport) taking into account boundary conditions;
Derivation and use of Integral Theorems: Green's formula, exact differential, Stokes theorem, Gauss theorem;
Introduction to vector calculus with examples (e.g. continuity equation).
Written Exam (2 Hours) May/June 90%
Coursework (Regular Problem Sheets) 10%