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| Module Delivery |
| Autumn semester |
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| Assessment Requirements |
Coursework: one class test 12.5%
one take home assignment 12.5%
Exam 75% |
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| Module Overview |
| This module builds on the level 1 module "Matrices and Linear ODEs" and considers qualitative and quantitative aspects of Ordinary Differential Equations |
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| Prerequisites/Co-requisites |
MS110 Matrices and Linear ODEs
MS113 Linear Algebra |
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| Module Aims |
| The aim of this module is to study both qualitative and quantitative aspects of Ordinary Differential Equations. |
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| Learning Outcomes |
By the end of the module a student should be able to:
- find exact solutions to certain types of differential equations;
- plot and interpret phase portraits on the line or in the plane;
- determine the stability of equilibria and periodic solutions.
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| Module Content |
- Scalar first-order differential equations; review of separable and linear equations.
- Phase portraits on the line; equilibria and their stability.
- Theorems on existence, uniqueness, continuous dependence on initial conditions.
- Linear, autonomous systems of differential equations: relation between stability and eigenvalues; classification of planar phase portraits.
- Nonlinear systems: equilibria and their classification, linear stability analysis, Lyapunov functions, phase portrait near an equilibrium.
- Periodic solutios and their stability: Poincare maps; introduction to Floquet theory.
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| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and example classes. Learning takes place through lectures, exercises (example sheets), preparation for tests and background reading.
There will be 3 contact hours for 10 weeks consisting of lectures, tutorials and example classes. |
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| Selected Texts/Journals |
- D..K. Arrowsmith and C.M. Place
Dynamical Systems: differential equations, maps and chaotic behaviour,
Chapman & Hall (1992)
- D.W. Jordan and P. Smith
Nonlinear Differential Equations
Oxford University Press (1987)
- M. Braun
Differential Equations and their Applications
Springer-Verlag (1993)
- R.K. Nagle and E.B. Saff
Fundamental of Differential Equations and Boundary Value Problems
Addison-Wesley (1993)
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| Last Updated |
February 2008 |
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