This course develops mathematical techniques which are useful in solving
`real-world' problems involving differential equations, and is a
development of ideas which arise in the second year differential
equations course. The course embraces the ethos of mathematical
modelling, and aims to show in a practical way how equations `work',
and what kinds of solution behaviours can occur.
The primary material for this course is section A differential
equations. The course provides a platform for B6 Fluid mechanics and
B8 Topics in applied mathematics, and for the fourth year courses
Mathematics and the Environment, Mathematical Physiology, and
Perturbation Methods. The introductory course B568 is essential.
Modelling, conservation and constitutive laws, nondimensionalization.
Partial differential equations: waves and shocks, similarity
Problem sheets numbered 2 to 8 cover material lectured in weeks
2 to 8, and
consist (more or less) of some of the exercises in the notes, and are
pdf format. Problem sheets 2 to 7
(sheet 2 is the first) are now ready.
Specimen finals questions
are available in
pdf format (as at 27/4/05, for
They are actually quite a bit longer and harder than fhs
questions. They are also out of date. If they get resurrected for this
year's syllabus, it will probably not be till March or April.
Lecture notes are available and can be downloaded in
pdf format. They are available at
A.C. Fowler 2005 Techniques of applied mathematics.
Mathematical Institute lecture notes.