Modelling with Differential Equations
| Code | School | Level | Credits | Semesters |
| MATH2035 | School of Mathematical Sciences | 2 | 20 | Full year China |
- Code
- MATH2035
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Full year China
Summary
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 MATH1027 and MATH1029. 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).
Target Students
Single Honours students from the School of Mathematical Sciences.
Classes
- One 1-hour seminar each week for 24 weeks
- One 2-hour lecture each week for 24 weeks
Activities may take place every teaching week of the Semester or only in certain weeks.
Assessment
- 10% Inclass Exam 1 (Written): Inclass test 1
- 10% Inclass Exam 2 (Written): Inclass test 2
- 80% Exam 1 (3-hour): Written examination
Assessed by end of spring semester
Educational Aims
Thismodule 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. Thismodule 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 will be able to:
L1 Analyse systems of ordinary differential equations using linearisation and phase plane techniques;
L2 Apply the method of characteristics to solve linear and nonlinear first-order partial differential equations;
L3 - Obtain the canonical form of linear second-order partial differential equations and hence solve hyperbolic and parabolic equations;
L4 - Derive and solve a simple model equation for traffic flow;
L5 - Derive pathlines and streamlines for two-dimensional fluid flows;
L6 - Derive and apply Bernoulli's equation for steady fluid flow.
Conveners
- Dr Hayk Mikayelyan