Lecture Notes:
Linear stability theory
Section
1: Introduction
Section
2: Thermal instabilities
Section
3: Centrifugal instabilities
Section
4: Shear instabilities
Nonlinear stability theory
Sections 5 and
6: Introduction and review of nonlinear stability theory
Section 7: Local bifurcation theory
Section 8: The Stuart-Landau equation
Section 9: The Ginzburg-Landau equation
Example sheets:
Linear stability analysis:
Example Sheet for Part I: Linear Stability Analysis Additional basic example
Answers Q1 to Q3 Answers Q4 to Q6 Answers Q7 to Q8 Answer to additional example Answers Q9 to Q11 Answers Q12 to Q14
Nonlinear stability analysis:
Example 1 Example 2 Example 3 Example 4
Answers 1 Answers 2 Answers 3 Answers 4
Additional material for MATH45132/MATH65132:
Numerical solution of an eigenvalue problem
Imperfections in Stuart-Landau equations
Coursework:
Coursework scripts will be handed out in the example class in Week 5,
and will be collected by Tuesday of Week 8.
MATH35132 MATH45132/MATH65132
Exam scripts 2008-2011:
2008-2009
2009-2010
MATH35132 2010-2011
MATH45132/MATH65132 2010-2011
Exam rubric 2012:
Page last updated 24 April 2012
Send any comments or questions to ajuel@ma.man.ac.uk