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Curricular information is subject to change
On completion of this module students should be able to:
1) Construct intermediate linear and nonlinear mathematical models, based on concepts such as dimensional analysis and the continuum hypothesis.
2) Solve differential equations analytically, using methods such as:
Partial fraction decomposition.
Separation of variables.
Chain rule.
Nonlinear mappings.
Characteristic equation method.
Integrating factor method.
Phase-plane analysis: Critical points; separatrices; linearisation near critical points.
Matrix methods.
3) Analyse properties of the solutions and describe the meaning of the solutions for the phenomena studied. Applications may include:
One-dimensional mechanical systems (linear and nonlinear).
The falling skydiver.
Nonlinear motion of a projectile.
Resonant systems with external forcing.
Nonlinear high-dimensional models such as the prey-predator model.
Population models: The effect of harvesting; the tragedy of the commons.
The famous Lorenz 3D atmospheric model leading to chaotic orbits.
The Brusselator and other chemical clocks.
Student Effort Type | Hours |
---|---|
Specified Learning Activities | 24 |
Autonomous Student Learning | 40 |
Lectures | 36 |
Tutorial | 12 |
Total | 112 |
Not applicable to this module.
Description | Timing | Component Scale | % of Final Grade | ||
---|---|---|---|---|---|
Examination: End of Trimester Exam | 2 hour End of Trimester Exam | No | Standard conversion grade scale 40% | No | 60 |
Continuous Assessment: In class tests & WeBWorK automatic assignments | Varies over the Trimester | n/a | Standard conversion grade scale 40% | No | 40 |
Resit In | Terminal Exam |
---|---|
Autumn | Yes - 2 Hour |
• Group/class feedback, post-assessment
• Online automated feedback
Group/class feedback, post-assessment: This is implemented by the lecturer and tutors, who will go through solutions of selected problems. Online automated feedback: This is implemented in the context of WeBWorK automatic assessment (gradable), which tells the student whether their answers are correct or not.
Name | Role |
---|---|
Ms Niamh Fennelly | Tutor |