MATHEMATICAL AND COMPUTATIONAL PHYSICS - 2027/8

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
• Fundamental topics in computational physics such as root finding, finding eigenvalues of matrices etc
• Basic data analysis, such as fitting of simple functions to noisy data

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 and data analysis problems

• ability to tackle unseen mathematical problems using known methods

   

  Thus, the summative assessment for this module consists of:

• Computational assignments spanning numerical mathematics and data analysis. Assessment and feedback are focused on the correctness of calculations, and 
  understanding the results, any use of Large Language Models (LLMs) in code writing and why the code is correct 
• a mid-semester mathematics test (1 hr)
• a final examination in mathematics (1.5 hrs)

Formative assessment & Feedback

Mock examination providing formative feedback. Continuous feedback given in supervised computational classes. Verbal feedback is given in tutorial sessions. 

Mid-semester maths test provides feedback as well as contributing to the summative assessment.

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. 
• teach students how to produce, debug and test scientific code, including code writing with the assistance of Large Language Models as appropriate
• teach students to present results from code in professional-looking plots
  

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

The learning and teaching methods include:

• 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 2027/8 academic year.