MATHEMATICAL AND COMPUTATIONAL PHYSICS - 2024/5

Module Overview

This module builds on the Essential Mathematics module to develop further mathematical and computational skills as an aid to understanding and exploring physics concepts. The mathematics Units of Assessment are taught in lecture-based classes with associated workshop sessions, and cover multi-variable calculus, Fourier Series

The computational part of the course consists of a series of assessed exercises, with classroom support, which develop computational problem solving skills, and link in with the mathematics covered elsewhere in the module and in the prerequisite module.

Module provider

Mathematics & Physics

Module Leader

DIAZ TORRES Alexis (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

None

Module content

Indicative content includes:

• Mathematical Physics:


• Functions of two or more variables.  Partial derivative, chain rule, changing variables and Taylor’s theorem. Gradient. Identifying maxima, minima and saddle points, Lagrange multipliers.


• First-order differential equations; the method of separation of variables and integrating factors.  Exact differential equations.  Simple second order equations with constant coefficients.  General and particular solutions. Series solutions to second order equations. Laplace transform and its applications.


• Selected topics of linear algebra: eigenvectors and eigenvalues, similarity transformations, diagonalisation of matrices, simultaneous linear equations, rotational matrices, normal modes.


• Fourier Series; orthogonal functions, computation of Fourier coefficients.


• Line integrals, multiple integrals; double and triple integrals, changes of variables, the Jacobian; the use of spherical and cylindrical coordinates.

• Computational Physics


• The Computational Physics part of the module consists of the following 5 assignments:


• Newton-Raphson root finding


• Finite difference methods


• Series computing


• Geometric matrix-vector operations


• Linear algebra

Assessment pattern

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

• 
  recall of subject knowledge
  


• 
  ability to apply individual components of subject knowledge to basic situations
  


• 
  ability to design and implement computational solutions to given mathematical problems
  


• 
  ability to tackle unseen mathematical problems using known methods
  
   
  
  Thus, the summative assessment for this module consists of:
  


• 
  5 computational exercises covering different programming skills, and surveying different areas of the mathematics syllabus with deadlines spread equally throughout semester
  


• 
  a mid-semester mathematics test (1 hr)
  


• 
  a final examination in mathematics (1.5 hrs)
  

Module aims

• enable students to classify and solve simple first- and second-order ordinary differential equations.
• Enable students to compute the coefficients of Fourier series.
• provide an understanding of functions of more than one variable, their derivatives, and the location stationary points of functions of two variables, and to be able to classify them as maxima, minima or saddle points.
• enable the use multiple integrals to calculate surface and volume properties
• develop skills in and experience of developing computational solutions to problems in mathematics and physics. 
• produce well-structured and well-though-out program solutions to problems, drawing on examples from the mathematical physics part of the module,
• present results from the programs in appropriate graphical format.

Learning outcomes

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• equip students with subject knowledge


• develop skills in applying subject knowledge to unseen problems in mathematics, including problems with a direct physical application


• ensure that students are able to take problems in

• Lecture and tutorial classes in mathematics


• Supervised computational laboratory sessions 


• Independent study

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: PHY1038

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability, and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: Throughout the module students will develop their computational skills in solving mathematical exercises using Python.

Resourcefulness and Resilience: Problem solving is a key component of this module with students given the opportunity to tackle mathematical exercises in tutorials using analytical methods learned at lectures.

Programmes this module appears in

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.