Pre-requisite: MAST4006 (Mathematical Methods 1)
OverviewThis module introduces the basic ideas to solve certain ordinary differential equations, like first order scalar equations, second order linear equations and systems of linear equations. It mainly considers their qualitative and analytical aspects. Outline syllabus includes: First-order scalar ODEs; Second-order scalar linear ODEs; Existence and Uniqueness of Solutions; Autonomous systems of two linear first-order ODEs.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
E. Kreyszig, Advanced Engineering Mathematics (10th edition), John Wiley, 2011
Robert L. Borrelli, Courtney S. Coleman, Differential Equations: A Modeling Perspective, 2nd Edition (ISBN: 978-0-471-43332-3), 2004.
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within ordinary partial differential equations (ODEs);
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: phase portraits, stability of fixed points, the Frobenius method, autonomous linear systems of ODEs;
3 apply the concepts and principles in basic ODE methods in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.
The intended generic learning outcomes. On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.