Announcements


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).

Forum

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
Email A.M.Rucklidge@leeds.ac.uk
Phone (0113) 3435161
Interests Pattern Formation, Nonlinear Dynamics, Astrophysical Fluid Dynamics
vcard
Photo of Alastair Rucklidge


Students


Photo of Abeer AL-NAHDI
Abeer AL-NAHDI
(Leeds)
Photo of Chris Bennett
Chris Bennett
(Birmingham)
Photo of Michael Bennett
Michael Bennett
(Cardiff)
Photo of Gokcen Cekic
Gokcen Cekic
(Birmingham)
Photo of David Dowell
David Dowell
(Loughborough)
Photo of Sam Durston
Sam Durston
(Exeter)
Photo of Matthew Edgington
Matthew Edgington
(Reading)
Photo of Mark Esson
Mark Esson
(Birmingham)
Photo of Meurig Gallagher
Meurig Gallagher
(Birmingham)
Photo of Mariano Galvagno
Mariano Galvagno
(Loughborough)
Photo of Kavita Gangal
Kavita Gangal
(Newcastle)
Photo of Esen hanac
Esen hanac
(Birmingham)
Photo of Aniayam  Okrinya
Aniayam Okrinya
(Loughborough)
Photo of Robert Pattinson
Robert Pattinson
(Newcastle)
Photo of Shaker Rasheed
Shaker Rasheed
(Nottingham)
Photo of Kenneth  Uda
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

Bibliography


Elements of applied bifurcation theory Kuznetsov
Note:

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 (980.8 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 (959.8 days ago)


Example Sheet 3

Files:Exam paper
Deadline: Monday 16 January 2012 (924.8 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.txtL
1-10ds1.pdfL
1-5examples_1.pdfL