To transform, try a good workout

The target audience, says author J. David Logan, is students "without the time or desire" to read larger calculus-based texts or to "explore internet supplements". Undergraduate mathematics sections in UK campus bookshops are shrinking as universities increasingly require lecturers to produce printed notes as a minimum for fee-paying students.

When many are in effect writing camera-ready manuscripts, one wonders what the future is for such introductory books.

Nevertheless, Logan has produced a well-crafted text, densely packed with interesting applications from diverse fields. The chapters cover (ordinary) differential equations, analytical solutions and approximations, second-order differential equations, Laplace transforms, linear and nonlinear systems.

The material is well presented and introduces new concepts such as the phase plane, simple numerical techniques, powers series solutions and equations such as Airy's and Bessel's. Some knowledge of mechanics might be helpful, but the necessary background is explained. Later chapters move to more advanced ideas, touching on Van der Pol, Duffing equations and Hamiltonian systems. The book could be used to offer an appetiser for later courses, but in the UK it is probably more suited to mathematicians.

Returning to the target audience, perhaps Logan might share Einstein's view that "any man who reads too much and uses his own brain too little falls into lazy habits of thinking". The text will certainly provide a good mental workout.

Christopher Howls is senior lecturer in applied mathematics, Southampton University.