Mathematics for Chemistry / Physics
SCQF Level 9
Academic year(s): 2019-2020
SCOTCAT credits : 20
ECTS credits : 10
Level : SCQF Level 9
Availability restrictions: Available only to Chemistry and Physics MSci students
This module consists of the content and assessment of all of PH3081 and the first part of PH3080. The module aims to develop mathematical techniques that are required by a professional physicist or astronomer. There is particular emphasis on the special functions which arise as solutions of differential equations which occur frequently in physics, and on vector calculus. Analytic mathematical skills are complemented by the development of computer-based solutions. The emphasis throughout is on obtaining solutions to problems in physics and its applications. Specific topics to be covered will be Fourier transforms, the Dirac delta function, partial differential equations and their solution by separation of variables technique, series solution of second order ODEs, Hermite polynomials, Legendre polynomials and spherical harmonics. The vector calculus section covers the basic definitions of the grad, div, curl and Laplacian operators, their application to physics, and the form which they take in particular coordinate systems. In the other section of the module students are introduced to the Mathematica package, and shown how this can be used to set up mathematical models of physical systems.
Pre-requisite(s): Before taking this module you must pass PH2012 and pass MT2501 and pass MT2503. Entry to MSci Chemistry and Physics degree programme
Anti-requisite(s): You cannot take this module if you take PH3080 or take PH3081 or take MT3506
Weekly contact: 3 x 1-hour lectures (x 10 weeks), 2 x 2-hour PC Classroom supervised sessions (x 5 weeks), 1-hour tutorial (x 5 weeks)
Scheduled learning hours: 57
Guided independent study hours: 143
As used by St Andrews: 2-hour Written Examination = 60% Coursework = 40%
As defined by QAA
Written examinations : 71%
Practical examinations : 22%
Re-assessment: Oral Re-assessment, capped at grade 7
Module coordinator: Dr C A Hooley
Module teaching staff: Dr C Hooley, Dr M Mazilu, Dr A Gillies
physics and astronomy modules.
You will have acquired the ability to program in Mathematica and be able to use Mathematica to solve, visualise and gain insight into a variety of physical problems. You will be aware of the advanced capabilities of Mathematica including symbolical and numerical equation solving.
By the end of the semester students are expected to be able to:
For the part of the module overlapping with PH3081:-
Dirac delta function
Series solutions, Hermite polynomials
Laplace’s equation in Cartesian and spherical coordinates
Legendre polynomials, spherical harmonics
Gradient, directional derivatives
Line and surface integrals
Divergence, divergence theorem
Curl, Stokes’ theorem
Helmholtz theorem, the Maxwell equations
Vector integration techniques
For the part of the module overlapping with PH3080:-
There are introductory programming labs teaching basic programming skills in Mathematica, different numerical methods and setting up physical problems. There are 5 case study labs and 3 assessed homework tasks. These are designed to provide case studies illustrating the use of Mathematica to solve and visualise a variety of Physics problems as well as introducing a number of advanced features in Mathematica. The case studies can vary from year to year but past case studies have included: Solving differential equations, Fourier transforms for filtering, chaotic motion, Mechanics and motion of coupled bodies moving in a potential, Analysis of periodic structures and Matrix and Tensor manipulation.
Indicative timetable: S1 weeks 1-2: introduction, S1 weeks 3-8: case studies, S1 week 9: class test
Additional information on continuous assessment etc.
Please note that the definitive comments on continuous assessment will be communicated within the module. This section is intended to give an indication of the likely breakdown and timing of the continuous assessment.
This module is formed from all of PH3081 Maths for Physicists and part of PH3080 Computational Physics. Two thirds of the module credit comes from the PH3081 part, and one third from the activities that are shared with PH3080. These two component parts are in the core JH programme, and as such there is a summary of deadlines etc. on the School’s Students and Staff web pages. Please see those module synopses for more details.
This module contains material that is or may be part of the IOP “Core of Physics”. This includes
Three dimensional trigonometry
Vectors to the level of div, grad, and curl, divergence theorem and Stokes’ theorem
Fourier series and transforms including the convolution theorem
Please view University online record:
Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.