Mathematical Physics

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:5
Terms in which taught: Spring / Summer term module
Pre-requisites: MA1CA Calculus and MA1LA Linear Algebra and PH101 Physics of the Natural World or MA1MM Mathematical Modelling
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Module version for: 2016/7

Summary module description:
The course continues the applied stream of mathematical education from e.g. mathematical modelling and enables one to choose more detailed physics-related modules in the third and fourth years. The overarching theme connecting these will be different forms of energy governing the processes under consideration. What is the relevance of calculus, ODEs and PDEs to real life? The majority of these mathematical concepts were created to describe (or model) processes of nature. For example problems like sound wave propagation or heat transfer have led to partial differential equations. In this module you will study how different mathematical concepts arise from physical phenomena, and in particular discover that completely different areas of physics can be described by exactly the same mathematical equations. Note that this course will be very different from A-level physics: it will focus on the mathematical aspects of physics, i.e. the physics useful for understanding mathematics, whereas A-level physics avoided mathematics at all costs.
Aims:
1. Break down possible barriers between physics and mathematics, learn their differences and
similarities and thus be able to translate from one level of description to another.

2. Build up mathematical intuition from analogies with physical problems. Absolute majority of
good mathematicians use physical analogies to guide their research.

3. Familiarize students with the main concepts of theoretical physics to broaden their horizons.

4. Provide motivation and connections for other modules and to explain the practical applications of undergraduate mathematics studied in the department.

Assessable learning outcomes:
By the end of the module students will be familiar with the concepts of units, dimensional analysis and well-defined physical laws. They will be able to apply them to analyse physical descriptions and formulate well-defined mathematical problems based on the descriptions.

The main skill we will be developing during the module is the ability to separate important factors
from the unimportant ones and to create models of different levels of sophistication. We will study this using examples from heat transfer and mass diffusion.
Additional outcomes:
Confidence in facing real world probems.

Outline content:
System of units, class of system of units and dimensional monomial theorem,
Dimensions, physical laws and pi-theorem,
Conservation of mass and diffusion,
Non-linear diffusion versus linear diffusion: similarities and differences,
Diffusion in a composite medium, convection-diffusion
Conservation of energy and thermal conductivity,
Thermal conductivity in composite media
Physical origin of the boundary conditions in the description of diffusion and thermal conductivity
Conditions on the moving boundaries with the phase transitions - melting, solidification and chemical reactions

Brief description of teaching and learning methods:
Lectures, supported by problem sheets and lecture-based tutorials.

Contact hours:
Lectures- 20
Tutorials- 10
Guided independent study- 68
Total hours by term- 98
Total hours for module- 100

Summative Assessment Methods:
Written Exam- 70%
Written assignment including essay- 30%

Other information on summative assessment:
Three assignments (10% each) and one examination.

Formative assessment methods:
Problem sheets.

Length of examination:
2 hours.

Requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).