|Title: Practical Applied Mathematics: Modelling, Analysis, Approximation|
|Author: Sam Howson|
|Reviewer: David Jefferies|
|Publisher: Cambridge University Press|
|ISBN: 0 521 84274 3 and 60369 2|
|Price: £65.00 and £29.99|
This excellent little book prompts one to "ask for more" - unlike most technical university-level applied mathematics books, to which my own reaction is too often "how overblown".
Drawing from a wide variety of topics to which mathematics is often applied "in the real world", the textbook tries to put "flesh on the bare bones of equations" in a way that will appeal to the student and the user. It is a nearly ideal introduction to the practical world of mathematical modelling for the neophyte, and the many applications are used to show that applied mathematics is much more than a series of "academic calculations".
Mathematical techniques covered include distributions, ordinary and partial differential equations, asymptotic methods, expansions and the basis of modelling science. Applications are given to piano tuning, hot strip mill steel continuous casting, egg turning during incubation, traffic flow, the pantograph and the mathematics underpinning computer animations of human models' hair.
The applications that appealed to me included the description of piano-tuning, which extended the usual discussion to the effect of bending stiffness of the strings and the stretching of the equal-tempered scale by the piano tuner that is an automatic consequence of this. After that, the turning of birds' eggs during incubation - why do the birds do it and what advantages does it confer? And then, the solidification of a continuous strip of molten steel being drawn from a tundish in a continuous casting plant, which is the most modern way of making steel strip economically.
The writing is accessible: informal (with side-notes) but not superficial.
The examples are chosen to illustrate the techniques under discussion, but they are of such interest in their own right that they motivate the student to take a deeper look at the underlying mathematics. As the author says in his preface, "almost any physical situation has some mathematical interest".
This book deserves a permanent place on the shelves of any university academic who has to teach scientists (hard or soft) and engineers (all disciplines) to use their mathematics creatively. It is the perfect answer to those students who complain about lack of relevance in their undergraduate mathematics courses.
It is best served up with an accompaniment of more formal texts covering differential vector algebra (div, grad, curl) and the basics of differential equations, statistics and distributions. The book stops short of discussing the kind of chaotic dynamics that happen in many non-linear problems.
David Jefferies is senior lecturer in engineering, Surrey University.