David Acheson

From Calculus to Chaos

The aim of David Acheson's book: From Calculus to Chaos:An Indroduction to Dynamics is to make the mathematics of dynamical systems available to a wider audience than those choose to study it at university.

Acheson has taken on a challenging task, but I felt that he succeeded very well. It's not a book for math-phobics - 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.

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Paperback 280 pages
ISBN: 0198500777
Salesrank: 606300
Weight:1.1 lbs

Published: 1998 Oxford University Press, USA

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Amazon.co.uk info

Paperback 280 pages
ISBN: 0198500777
Salesrank: 211203
Weight:1.1 lbs

Published: 1997 OUP Oxford

Amazon price £23.75

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Paperback 280 pages
ISBN: 0198500777
Salesrank: 708105
Weight:1.1 lbs

Published: 1997 Oxford University Press

Marketplace:New from CDN$ 54.79:Used from CDN$ 23.50

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Product Description
What is calculus really for? This book is a highly readable introduction to the applications of calculus, from Newton's time to the present day. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts.

Product Description

What is calculus really for? This book is a highly readable introduction to the applications of calculus, from Newton's time to the present day. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts.

Recommended ****
The author manages to express in an easily understandable form many of the more interesting applications of calculus, from planetary motion to the Indian Rope Trick (almost). This book is ideally suited for first year undergraduates and sixth-formers with a strong interest in Mechanics. All those doing maths at Oxford University MUST buy this book (the author spends most of the lectures making references to it and to not buy the book would be to not understand the mechanics course).

Recommended ****

The author manages to express in an easily understandable form many of the more interesting applications of calculus, from planetary motion to the Indian Rope Trick (almost). This book is ideally suited for first year undergraduates and sixth-formers with a strong interest in Mechanics. All those doing maths at Oxford University MUST buy this book (the author spends most of the lectures making references to it and to not buy the book would be to not understand the mechanics course).

I have also been to Dr. Acheson's lectures ***
I think that the previous reviewer was a little optimistic. Acheson is a reasonable lecturer and this book does follow the first part of the Oxford University mathematics first year mechanics course well (in fact some of his problem sheets come straight from the book making it easy to complete said problem sheets!). However, the book goes into lots of, although interesting, unnecessary detail. It also does not contain anything on rotating frames of reference which is in the mechanics course at Oxford. So my advice is not to buy this book as a course guide but to get "A first course in Mechanics" by Lunn instead. However, if you want to get this book for interest then it is well worth it.

I have also been to Dr. Acheson's lectures ***

I think that the previous reviewer was a little optimistic. Acheson is a reasonable lecturer and this book does follow the first part of the Oxford University mathematics first year mechanics course well (in fact some of his problem sheets come straight from the book making it easy to complete said problem sheets!). However, the book goes into lots of, although interesting, unnecessary detail. It also does not contain anything on rotating frames of reference which is in the mechanics course at Oxford. So my advice is not to buy this book as a course guide but to get "A first course in Mechanics" by Lunn instead. However, if you want to get this book for interest then it is well worth it.

I've been to this guy's lectures ****
He's a good lecturer, doing the 1st term mechanics course (maths, the previous reviewer should note) at Oxford, much of which (and more) is covered in this book. And the book is quite decent too, especially for those such as myself who dislike mechanics dreadfully and who think it should be an option rather than an imposition - for goodness sakes, as the other reviewer implies, it just isn't maths. Still, if you are doing first year mechanics, buy this book - he has some great ideas and methods.

I've been to this guy's lectures ****

He's a good lecturer, doing the 1st term mechanics course (maths, the previous reviewer should note) at Oxford, much of which (and more) is covered in this book. And the book is quite decent too, especially for those such as myself who dislike mechanics dreadfully and who think it should be an option rather than an imposition - for goodness sakes, as the other reviewer implies, it just isn't maths. Still, if you are doing first year mechanics, buy this book - he has some great ideas and methods.

Excellent "interactive" introduction to nonlinear dynamics *****
This is an excellent overview of dynamics from the birth of calculus to the latest research in nonlinear dynamics - it bears all the marks of being well-honed under the test of teaching the material to students. As a physicist, Acheson doesn't get hung up on mathematical niceties at the expense of the meaning of things. A great feature is the inclusion of little computer programs written in QBASIC so that you can explore things for yourself. In the mid-1980s there were dozens of books that took this programming approach; all power to Acheson for reviving it in the face of "multimedia maths".

Excellent "interactive" introduction to nonlinear dynamics *****

This is an excellent overview of dynamics from the birth of calculus to the latest research in nonlinear dynamics - it bears all the marks of being well-honed under the test of teaching the material to students. As a physicist, Acheson doesn't get hung up on mathematical niceties at the expense of the meaning of things. A great feature is the inclusion of little computer programs written in QBASIC so that you can explore things for yourself. In the mid-1980s there were dozens of books that took this programming approach; all power to Acheson for reviving it in the face of "multimedia maths".