Four of the scheduled lectures will have to be re-arranged. The lecture scheduled for Friday 21st will be at 1pm on Friday 28th instead. Those scheduled for the 2nd, 9th and 16th December will also be rearranged (probably for 1-2pm on Fridays 4, 11, 18 November).
The material for the 10 lectures is now on the web, as is example sheet 1 (due 14 November).
General
This course is part of the MAGIC core.
Description
Many problems in Applied Mathematics are nonlinear and described by nonlinear ordinary (or partial) differential equations. This course aims to introduce students to the tools and techniques needed to understand the dynamics that might be found in such systems. The emphasis will be on concepts and examples rather than theorems and proofs, and will include a brief survey of useful numerical methods and packages. Students will be invited to submit examples of their own for possible discussion.
Semester
Autumn 2011 (Monday, October 10 to Friday, December 16)
Timetable- Fri 09:05 - 09:55
Lecturer
Alastair Rucklidge
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Students
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Abeer AL-NAHDI
(Leeds) |
Chris Bennett
(Birmingham) |
Michael Bennett
(Cardiff) |
Gokcen Cekic
(Birmingham) |
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David Dowell
(Loughborough) |
Sam Durston
(Exeter) |
Matthew Edgington
(Reading) |
Mark Esson
(Birmingham) |
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Meurig Gallagher
(Birmingham) |
Mariano Galvagno
(Loughborough) |
Kavita Gangal
(Newcastle) |
Esen hanac
(Birmingham) |
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Ummu Atiqah Mohd Roslan
(Exeter) |
Aniayam Okrinya
(Loughborough) |
Robert Pattinson
(Newcastle) |
Shaker Rasheed
(Nottingham) |
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Francesca Sage-Ling
(Surrey) |
Bartosz Szczesny
(Leeds) |
Kenneth Uda
(Loughborough) |
Prerequisites
No prerequisites information is available yet.
Syllabus
Outline syllabus
* Definition of a flow (ordinary differential equation), invariant sets, limit sets
* The Poincaré Map
* Equilibria, linearisation, stability of equilibria, periodic orbits and other invariant sets
* Structural stability, Hartman-Grobman Theorem, stable and unstable manifolds
* Centre manifold theorem, local bifurcations of equilibria and periodic orbits, Birkhoff normal form transformations for equilibria
* Example: the saddle-node-Hopf bifurcation (or other examples according to suggestions)
* Global bifurcations in two dimensions: derivation of the Poincaré map, leading on to Dynamical Systems II (maps). Discussion of the three-dimensional case and chaos
* Brief discussion of dynamics of dissipative PDEs (partial differential equations), pattern formation and the role of symmetry (probably will be omitted in 2011, but see the course on hydrodynamic stability theory, MAGIC014)
* Numerical and symbolic methods for ODEs and a mention of packages available. Continuation and the implicit function theorem
* Definition of a flow (ordinary differential equation), invariant sets, limit sets
* The Poincaré Map
* Equilibria, linearisation, stability of equilibria, periodic orbits and other invariant sets
* Structural stability, Hartman-Grobman Theorem, stable and unstable manifolds
* Centre manifold theorem, local bifurcations of equilibria and periodic orbits, Birkhoff normal form transformations for equilibria
* Example: the saddle-node-Hopf bifurcation (or other examples according to suggestions)
* Global bifurcations in two dimensions: derivation of the Poincaré map, leading on to Dynamical Systems II (maps). Discussion of the three-dimensional case and chaos
* Brief discussion of dynamics of dissipative PDEs (partial differential equations), pattern formation and the role of symmetry (probably will be omitted in 2011, but see the course on hydrodynamic stability theory, MAGIC014)
* Numerical and symbolic methods for ODEs and a mention of packages available. Continuation and the implicit function theorem
Bibliography
| Elements of applied bifurcation theory | Kuznetsov |
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)
Assessment
No assessment information is available yet.
Assignments
Example Sheet 1
| Files: | Exam paper | ||
| Deadline: | Monday 21 November 2011 (545.1 days ago) | ||
| Instructions: | I'm entering this on the system with an extended due date, since I've just figured out how to use the system! | ||
Example Sheet 2
| Files: | Exam paper | ||
| Deadline: | Monday 12 December 2011 (524.1 days ago) | ||
Example Sheet 3
| Files: | Exam paper | ||
| Deadline: | Monday 16 January 2012 (489.1 days ago) | ||
Files
Files marked L are intended to be displayed on the main screen during lectures.
| Week(s) | File | |
|---|---|---|
| 111125_notes.pdf | ||
| examples_2.pdf | ||
| examples_3.pdf | ||
| lorenz.py.txt | L | |
| 1-10 | ds1.pdf | L |
| 1-5 | examples_1.pdf | L |