Melina Freitag

Nonlinear Equations and Bifurcations (MA40050) Spring Term 2012

This is the website for the course MA40050 which can be taken as part of an MSc in Mathematics or an MMath degree. Prerequisites for the course are Analysis and Algebra as well as standard courses on Numerical Analysis and Numerical Linear Algebra.

Timetable

• Lectures: Monday 10.15 in 8W 1.34, Wednesday 12.15 in 1W 2.5 and Friday 3.15 in 8W 1.34
• Problem Classes: Wednesday and/or Friday(bi-weekly)

Some helpful links

• Unit decription (from catalogue)
• Martin Reed's notes on UNIX
• MATLAB Manual

Some suggested reading

• A. Spence, I.G. Graham: Numerical Methods for Bifurcation problems. pdf.
• J.E. Dennis, R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, New Jersey, 1983.
• C.T. Kelley: Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
• W.-J. Beyn, A. Champneys, E. Doedel, W. Govaerts, Yu. A. Kuznetsov, B. Sandstede Numerical continuation, and computation of normal forms. In: B. Fiedler (ed.) "Handbook of Dynamical Systems", v.2, Elsevier Science, North-Holland, 2002, pp. 149-219.

       and, for background reading on Numerical Linear Algebra,

• G. H. Golub, C. F. van Loan: Matrix Computations (3rd ed.) Johns Hopkins University Press Baltimore, MD, USA, 1996.

Lecture notes

• Cover Sheet
• Table of Contents
• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7

Handouts

• Introduction
• Handout 1 on Newton's Method in 1D.
• Handout 2 on the buckled beam problem.
• Handout 3 on the Contraction Mapping Theorem and the Implicit Function Theorem.
• Handout 4 on some background on linear algebra.
• Handout 5 on the graphical interpretation of the pseudo-arc-length method.
• Handout 6 on the pseudo-arc-length method applied to the Bratu problem.
• Handout 7 on some background on vector calculus.
• Handout 8 on the shooting method applied to a two-point boundary value problem.

Matlab codes

• Chapter 2: ex1.m, beam2.m, beam_n.m, ex2.m
• Chapter 4: bratu.m
• Chapter 7: shooting.m and the function file fun.m

Problem Sheets

If you would like individual feedback on your solutions to the problem sheets, please hand them in to the 4W Level 1 pigeon holes (there is a pigeon hole marked MA40050) by 7pm in the evening (latest) the night before the problem class.

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Problem Sheet 1 (Matlab codes ex1.m, ex2.m)				Solutions to Problem Sheet 1 (Matlab codes ex1mod.m, ex2mod.m)
Problem Sheet 2				Solutions to Problem Sheet 2
Problem Sheet 3 (Matlab codes ex3.m, beam2.m)				Solutions to Problem Sheet 3
Problem Sheet 4				Solutions to Problem Sheet 4
Problem Sheet 5				Solutions to Problem Sheet 5

Assignment

• Assignment set on Monday, 19th March 2012 and due Friday, 30th March 2012 at 3.00pm.
• The Matlab codes for the assignment can be found here.
• Coursework Cover Sheet

If you have any queries, please come and see me either after the lecture or in my office (1W 4.11) or send me an email.