MA5052 - Differential Equations (2019/20)
| Module specification | Module approved to run in 2019/20 | ||||||||||||
| 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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| Assessment components |
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| Running in 2019/20(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.
This module aims to give students a thorough understanding of the analytical techniques available to solve first and second order ordinary differential equations.
Prior learning requirements
Knowledge of First Year Calculus
Syllabus
Revision of first order ordinary differential equations: integrating factor method, separation of variables. LO1
Second order ordinary differential equations with constant coefficients. LO2, LO3, LO4, LO5
Second order ordinary differential equations of general, linear non-homogeneous form: reduction of order method. LO2, LO3
Euler's differential equation: elementary solution techniques about singular points. LO4
Series solution methods: series expansion about an ordinary point. LO4
Laplace Transform method: Solution of 1st and 2nd order differential equations LO5
Balance of independent study and scheduled teaching activity
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
Feedback to students for the Test is given in class and on weblearn. Feedback for Exam will be given after the assessment board.
Bibliography
Core Text:
Boyce, WE and Di Prima, RC (2012) Elementary Differential Equations John Wiley.
Recommended Reading:
Robinson, (2004) An Introduction to Ordinary Differential Equations, CUP
Earl A. Coddington, (1990), An Introduction to Ordinary Differential Equations, Dover Books on Mathematics