Credits:
 6 
Level:
 Honours (FHEQ level 6) 
Period: 
Semester 1

Assessment:
 EX 100% 
Supplementary Assessment:  Mandatory extra work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take PH20019 and take PH20020 
Description:
 Aims: The aims of this unit are to identify some of the issues involved in constructing mathematical models of physical processes, and to introduce major techniques of computational science used to find approximate solutions to such models.
Learning Outcomes: After taking this unit the student should be able to:
* dedimensionalise an equation representing a physical system;
* discretise a differential equation using grid and basis set methods;
* outline the essential features of each of the simulation techniques introduced and give examples of their use in contemporary science;
* use the simulation schemes to solve simple examples by hand.
Skills: Numeracy T/F A, Problem Solving T/F A.
Content: Construction of a mathematical model of a physical system (4 hours): Dedimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions.
Discretisation (2 hours): Grids and basis sets. Discretisation errors.
The finite difference method (4 hours): Review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications.
The finite element method (3 hours): Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications.
Introduction to computational methods for matrix problems (3 hours).
Molecular Dynamics and Monte Carlo methods (6 hours): Examples of Nbody problems, ensembles and averaging. The basic MD strategy. The basic MC strategy; random number generation and importance sampling. Applications in statistical mechanics. Simulated annealing. Computer experiments.

Programme availability:

PH30031 is Compulsory on the following programmes:
Department of Physics
 USPHAFB05 : BSc (hons) Physics with Computing (Fulltime)  Year 3
 USPHAKB06 : BSc (hons) Physics with Computing (with Placement) (Fulltime with Thick Sandwich Placement)  Year 4
 USPHAAB06 : BSc (hons) Physics with Computing with Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USXXAFM01 : MSci (hons) Mathematics and Physics (Fulltime)  Year 3
PH30031 is Optional on the following programmes:
Programmes in Natural Sciences
 UXXXAFB01 : BSc (hons) Natural Sciences (Fulltime)  Year 3
 UXXXAKB02 : BSc (hons) Natural Sciences with Industrial Placement (Fulltime with Thick Sandwich Placement)  Year 4
 UXXXAAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 UXXXAFM01 : MSci (hons) Natural Sciences (Fulltime)  Year 3
 UXXXAKM02 : MSci (hons) Natural Sciences with Professional Placement (Fulltime with Thick Sandwich Placement)  Year 4
 UXXXAAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM08 : MSc Modern Applications of Mathematics (Fulltime)  Year 1
 TSMAAFL02 : PG Dip Modern Applications of Mathematics (Fulltime)  Year 1
Department of Physics
 USXXAFB03 : BSc (hons) Mathematics and Physics (Fulltime)  Year 3
 USXXAKB04 : BSc (hons) Mathematics and Physics with Placement (Fulltime with Thick Sandwich Placement)  Year 4
 USXXAAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USPHAFB01 : BSc (hons) Physics (Fulltime)  Year 3
 USPHAKB02 : BSc (hons) Physics (with Placement) (Fulltime with Thick Sandwich Placement)  Year 4
 USPHAAB02 : BSc (hons) Physics with Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USPHAFB09 : BSc Physics (Fulltime)  Year 3
 USPHAKB09 : BSc Physics (with Placement) (Fulltime with Thick Sandwich Placement)  Year 4
 USPHAFM02 : MPhys Physics (Fulltime)  Year 3
 USPHAFM04 : MPhys Physics with Research Placement (Fulltime)  Year 3
