Manchester Est. 1824

MATH34011 : Asymptotic Expansions and Perturbation Methods

School of Mathematics, University of Manchester

Semester 1 2009-2010 Prof Bill Lionheart (updating in progress)

Course Information

Course information is on School of Maths Web site

Reading list

The John Ryland University Library's Link2Lists service has this Reading List. I have put some links to book sellers in the hope that it is helpful. Some carry used books that are cheaper. No endorsment of specific sellers is intended.

  1. J.G. Simmonds, J.E. Mann, A First Look at Perturbation Theory, Dover Publications, 1998 0486675513,9780486675510, GoogleBooks, Blackwell's
  2. D.W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations (Oxford Applied Mathematics and Computing Science Series), 1987, ISBN 019859657X,, New edition at Blackwell's online
  3. J.D. Murray: Asymptotic Analysis, Applied Mathematical Sciences, Vol. 48, Springer-Verlag, Berlin, Heidelberg, New York, 1984, ISBN 3540909370.
  4. A. Nayfeh, Introduction to Perturbation Techniques, Wiley, 1981. ISBN 0471310131

First six chapters of [1] and Chapter 1,2,3,4,5,6,9 of [2] contain all the information in this course.

[3] is more rigorous, not recomended as a first reading but useful after [1] is mastered. Similarly [4].

Some prerequite stuff

You should have done MATH10222 or MATHH10232: Calculus and Applications. Pay attention to the solution of constant coefficient ODEs with a non-zero right hand side. Especially in the degenerate case. See Ex Sheet 4 of 10222. Also damped motion in Ex5. Ex 6 on perturbations gives the beginning of ideas in this course. Similar examples in 10232 (you can look at notes for either). It will also help you to remember the examples of null sequences from Sequences and Series, although we will need these ideas for limits of functions, which you learnt in Real and Complex analysis (or equivalent), including L'Hopital's rule. Rod Haggarty is your friend here: Fundamentals of Mathematical Analysis, Addison-Wesley.


Solutions will appear about one week after the examples are set. Also I am working through the examples making corrections and changes about one week ahead. Look for the date at bottom.
Examples 1 Solutions 1 Mathematica Note book(save and then open with Mathematica)
Examples 2 Solutions 2
Examples 3 Solutions 3
Examples 4 Solutions 4
Examples 5 Solutions 5
Examples 6 Solutions 6 Ignore Q6!
Examples 7 Solutions 7
Examples 8 Solutions 8
Examples 9 We are not doing this sheet this year
Examples 10 Solutions 10
Some notes
Greg Astley has heroically typeset his notes for the course using LaTeX. I am working through checking them but Greg and I thought it might be helful for you to be able to see them anyway, before I have checked them, on the basis that they are mostly right and more eyes looking at them will catch errors anyway. This will be especially useful I hope to one of you who had their bag stolen with their 34011 notes in it from University Place! Please email me any updates. Notes here

Past exam papers 2006/07, 2007/08, 2008/09.(Scanned answers...and this page was misfed. Some older exams 1996, 1999, 2002