
David Acheson
From Calculus to Chaos
Acheson has taken on a challenging task, but I felt that he succeeded very well. It's not a book for mathphobics  there are plenty of equations in the book  but it made the subject accessible to anyone with a firm grasp of the later parts of school mathematics. A central theme in the book is the modelling of the equations using simple computer programs, and there are plenty of diagrams of the output, thus helping the reader to get a feel for what the equations are saying.
The book starts by considering differential equations in general, and moves on to those for simple oscillators such as pendulums. This is followed by a look at the motion of the planets. Acheson then describes the equations of waves and diffusion which leads on to a study of fluid flow. Now fluid flow can result in turbulence, and the later part of the book looks at the origins of instability and chaos. The final chapter is 'chaos in reverse'  how to stabilise an upside down pendulum. There are appendices with the QBasic programs used in the book (also available at http://home.jesus.ox.ac.uk/~dacheson/calchaos.html) and an introduction to the QBasic language. (The DOS based QBasic programs look very dated now though).
In summary, if you want a 'taster' of the mathematics of dynamics, or if you are interesting in the computer modelling of differential equations, then you should take a look at this book.