MA4J115 Continuum Mechanics
Introductory description
The modeling and simulation of fluids and solids with significant coupling and thermal effects is an important area of study in applied mathematics and engineering. Necessary for such studies is a fundamental understanding of the basic principles of continuum mechanics and thermodynamics. This course, which will closely follow the text "A first course in continuum mechanics'' by Andrew Stuart, is a clear introduction to these principles.
The outline will be as follows: we will begin with a review of tensor algebra and calculus, followed by mass and force concepts, kinematics, and then balance laws. We will then proceed to derive some commonly used models governing isothermal fluids and solids, consisting of systems of partial differential equations (PDEs). If time permits we will also explore the thermal case.
Module aims
To give students a clear theoretical background for models in continuum mechanics, which are the basis for many realworld engineering applications, and to develop an appreciation for the power of using physical principles to rigorously derive PDE models.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Tensors, their algebra and calculus.
 Forces, kinematics and balance laws.
 Derivation of models for isothermal fluids and solids.
 Solution of the model equations in some special cases.
Learning outcomes
By the end of the module, students should be able to:
 Manipulate tensors using their algebra and calculus
 Explain the physical concepts of mass, force, stress, deformation, displacement and strain as used in continuum modelling
 Apply physical principles including conservation of mass and momentum to derive general PDE balance laws
 Solve the resulting equations in some simple cases, and interpret these results to make physical predictions
Interdisciplinary
This module provides a rigorous mathematical approach to deriving partial differential equation models used in Physics, Engineering and Life Sciences, and so naturally connects with these disciplines.
Subject specific skills
Ability to apply tools of calculus to derive models fluid and solid systems
Ability to convert physical principles into mathematical equations
Ability to interpret mathematical models of the real world
Transferable skills
Ability to translate scientific ideas into mathematical language
Ability to communicate complex ideas and mathematical results clearly
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Private study  117 hours (80%) 
Total  147 hours 
Private study description
Homework problems.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group B1
Weighting  Study time  

Inperson Examination  100%  3 hours 
Standard 3 hour written exam.

Feedback on assessment
Written feedback on the outcome of the exam.
Courses
This module is Optional for:
 Year 1 of TMAAG1PE Master of Advanced Study in Mathematical Sciences
 Year 1 of TMAAG1P9 Postgraduate Taught Interdisciplinary Mathematics
 Year 1 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 1 of TMAAG1P0 Postgraduate Taught Mathematics
 Year 1 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics
This module is Option list A for:
 Year 2 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 2 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
 Year 4 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 4 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 5 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:
 Year 2 of TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
 Year 2 of TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)
 Year 4 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 3 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 4 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list C for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 4 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe
This module is Option list E for:
 Year 4 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 5 of USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated