## MATH34011 : Asymptotic Expansions and Perturbation Methods |

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

The John Ryland University Library's Link^{2}Lists 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.

- J.G. Simmonds, J.E. Mann, A First Look at Perturbation Theory, Dover Publications, 1998 0486675513,9780486675510, GoogleBooks, Blackwell's
- D.W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations (Oxford Applied Mathematics and Computing Science Series), 1987, ISBN 019859657X, GoogleBooksAmazon.com .co.uk, New edition at Blackwell's online
- J.D. Murray: Asymptotic Analysis, Applied Mathematical Sciences, Vol. 48, Springer-Verlag, Berlin, Heidelberg, New York, 1984, ISBN 3540909370.
- 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].

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 |

- Hand written summary notes of week 1
- Hand written summary notes of week 2
- A first example of using Mathematica with DSolve. PDF, Matheamtica notebook
- Week 3 (I am a bit behind). Exponential Integral Mathematica example pdf,nb
- The Truth About Nodes scanned handout.
- Mathematica notebook plot of Duffing's Eqn
- Formula sheet from 2009 exam. Trig identities etc.
- Quick summary of Lindstedt method
- Multiple scales DHM
- Multiple scales Van der Pol (lecture)
- Last year's revision guide and note on solving constant coef 2nd order ODEs with a RHS that is a solution of the homogeneous equation here . For this year easy integrals from Ex 3 are examinable, but "energy balance method" is not (just energy as a first integral as we did in the lecture to find a closed orbit).
- Scanned notes for Ch 7 the WKB method.

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