G12MDE Modelling with Differential Equations
(Last Updated:08 April 2013)

Year  13/14

Total Credits: 20

Level: Level 2

Target Students:  Single Honours and Joint Honours from the School of Mathematical Sciences. Available to JYA/Erasmus students.  Available to JYA/Erasmus students.

Taught Semesters:

Prerequisites: Knowledge of applied mathematics as covered in G11APP (or G11MOD) and knowledge of core mathematical concepts, methods and techniques as taught in G11ACF, G11CAL and G11LMA.

Corequisites:  

Summary of Content:  The success of applied mathematics in describing the world around us arises from the use of mathematical models, often using ordinary and partial differential equations. This module continues the development of such models, building on the modules G11CAL and G11APP. It introduces techniques for studying linear and nonlinear systems of ordinary differential equations, using linearisation and phase planes. Partial differential equation models are introduced and analysed. These are used to describe the flow of heat, the motion of waves and traffic flow. Continuum models are introduced to describe the flow of fluids (liquids and gases, such as the oceans or the Earth's atmosphere).

Method and Frequency of Class:

Method of Assessment: 

Convenor: 
Dr P Matthews
Dr G Adesso

Education Aims:  

This module aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations. This module leads to further study of mathematical models in medicine and biology and fluid mechanics. It also provides a foundation for further study of differential equations.

Learning Outcomes:  

A student who completes this module successfully should be able to:

Knowledge and understanding
use linearisation and phase plane techniques to analyse systems of ordinary differential equations;
solve the heat, wave and traffic-flow partial differential equations in one space dimension;
state standard mathematical results and relevant governing equations for inviscid flow;
use a range of mathematical techniques to solve simple problems describing inviscid incompressible flows.

Skills
reason logically, work analytically and justify conclusions using mathematical arguments with appropriate rigour;
work with abstract concepts and in a context of generality;
transfer expertise between different topics in mathematics ;
develop appropriate mathematical models and relate them to applications;
communicate results with clarity using appropriate styles, conventions and terminology;
use high level of numeracy and accuracy to solve complex problems;
select and apply complex concepts, appropriate methods and techniques to familiar and novel situations;
work effectively, independently and under direction;
adopt effective strategies for study.

Offering School:  Mathematical Sciences

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