MA307-7-AU-CO:
Advanced Ordinary Differential Equations and Dynamical Systems
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
Thursday 07 October 2021
Friday 17 December 2021
15
19 May 2021
Requisites for this module
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(none)
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The subject of Ordinary Differential Equations (ODEs) is a very important and fascinating branch in Mathematics. An abundance of phenomena in Physics, Biology, Engineering, Chemistry, Finance and Neuroscience to name a few, may be described and studied using such equations.
The module builds upon the 2nd-year MA202-5-SP-CO module on ODEs and will introduce students to advanced topics and theories in ODEs and dynamical systems Es.
The aim of the module is to familiarise students with advanced concepts and theories in Ordinary Differential Equations. It will also equip students with the knowledge and skills to solve such equations by using advanced analytical approaches.
1. Use methods to solve linear ODEs with variable coefficients
2. Systematic understanding of phase planes, population dynamics, prey-predator systems and other examples of dynamical systems.
3. Systematic understanding of Liapunov’s method and function
4. Systematic understanding of periodic solutions and limit cycles
5. Critical awareness on plane autonomous systems and linearisation
6. Systematic understanding of autonomous systems, almost linear systems, nonlinear systems, and stability/instability
7. Systematic understanding and use of the Laplace transform to solve initial value problems for linear differential equations with constant coefficients
The module will be based on the following syllabus:
1. Linear ODEs with variable coefficients (power-series solutions, singular points)
2. The phase plane: Linear Systems
3. Autonomous Systems and Stability
4. Locally linear systems
5. Examples of locally linear systems: competing species, predator-prey equations
6. Liapunov’s second method
7. Periodic solutions and limit cycles. The Poincaré-Bendixson theorem
8. The Laplace transform
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
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| Exam |
Main exam: 180 minutes during Summer (Main Period)
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Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Chris Antonopoulos, email: canton@essex.ac.uk.
Dr Chris Antonopoulos
canton@essex.ac.uk
Yes
No
Yes
Prof Stephen Langdon
Brunel University London
Professor
Available via Moodle
Of 88 hours, 86 (97.7%) hours available to students:
0 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.
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