MA5052 - Differential Equations (2017/18)
| Module specification | Module approved to run in 2017/18 | ||||||||||||
| Module title | Differential Equations | ||||||||||||
| Module level | Intermediate (05) | ||||||||||||
| Credit rating for module | 15 | ||||||||||||
| School | School of Computing and Digital Media | ||||||||||||
| Total study hours | 150 | ||||||||||||
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| Running in 2017/18(Please note that module timeslots are subject to change) |
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Module summary
The module extends the students’ knowledge of the techniques of calculus and introduces the concept of differential equations.
Prior learning requirements
Knowledge of First Year Calculus
Module aims
This module aims to give students a thorough understanding of the analytical techniques available to solve first and second order ordinary differential equations.
Syllabus
Revision of first order ordinary differential equations: integrating factor method, separation of variables.
Second order ordinary differential equations with constant coefficients.
Second order ordinary differential equations of general, linear non-homogeneous form: reduction of order method.
Euler's differential equation: elementary solution techniques about singular points.
Series solution methods: series expansion about an ordinary point.
Laplace Transform method: Solution of 1st and 2nd order differential equations
Learning and teaching
Students’ learning is directed via face-to-face learning activities centred on lectures and seminars. There is full provision of documents related to the module in electronic format that can be accessed by students at all times. The documents include lecture notes, slides, guidance to further reading and relevant mathematical packages, and exercises and tests.
Learning outcomes
On successful completion of this module, students should be able to,
LO1. Solve first order ordinary differential equations.
LO2. Solve second order ordinary differential equations with constant coefficients, involving initial value problems.
LO3. Solve second order linear ordinary differential equations by the method of reduction of order.
LO4. Solve Euler’s Equation, including solutions about singular points.
LO5. Solve first and second order ordinary differential equations by the Laplace Transform method.
Assessment strategy
The test will provide students with formative feedback and an opportunity to monitor their progress and create their study plan (LO1-LO2).
The final examination is a summative assessment (LO1-LO5). A full range of analytical solution methods as well as clarity of mathematical presentation will be assessed in the examination questions
Bibliography
1) Boyce, WE and Di Prima, RC (2012) Elementary Differential Equations John Wiley.
2) Robinson, (2004) An Introduction to Ordinary Differential Equations, CUP
3) Earl A. Coddington, (1990), An Introduction to Ordinary Differential Equations, Dover Books on Mathematics