Science for submarine spotters

It seems to be the fashion now to cover the entire syllabus from the first year of a degree course in one moderately sized, moderately priced text. I had to buy dedicated books on specific topics and often used only a fraction. Although some have been useful since, others have remained untouched. As most of today's physics graduates will not be academics or even professional physicists, it makes sense to buy comprehensive volumes instead of texts on individual topics.

The potential disadvantage is the lack of depth in each chapter. I can imagine that anyone finding Jerold Touger's book to their liking would probably also cope with John Cutnell and Kenneth Johnson's text, but would struggle with the books by David Halliday et al and Raymond Serway and John Jewett. The last two, which seem more suited to UK undergraduates, are at an obviously higher level, though all four seem at first sight to be covering similar material.

This said, Touger has written a very good book. It contains 28 chapters covering mechanics, properties of matter, thermodynamics and kinetic theory, vibrations and waves, electricity and magnetism and 20th-century physics. Included in this last are relativity, atomic and nuclear physics and quantum physics. The subtitle, Building Understanding , accurately reflects what the book is trying to achieve. There is an easy-going but detailed style of explanation, with the emphasis on concepts before mathematics. The reader is helped by diagrams, worked examples, conceptual problems and end-of-chapter problems. There are also some fantastic photographs: the image of light diffracted from the edge of a razor blade is quite stunning.

The main difficulty with Touger's book is knowing who it is aimed at. Many diagrams are in a cartoon style, clearly intended to appeal to a young readership. This is an algebra-based rather than calculus-based text - not a distinction made at undergraduate level in the UK - and my impression is that it was written for a US student market. I would be happy if our students had a good grasp of the material covered by Touger, but would hope that much of the knowledge had already been acquired. Good though the material is, it does not go far enough for university-level students.

Cutnell and Johnson cover similar material at a similar level, but aim at a more mature readership. Their explanations, also algebra-based, are clear and progressive. There are diagrams and photographs, an emphasis on concepts before mathematics, and lots of worked examples and end-of-chapter problems. Touger has "stop and think" items, which are conceptually challenging points of interest; Cutnell and Johnson offer conceptual examples that really do make you think. In the chapter on simple harmonic motion, there is an item about the spring constant showing that if the length of the spring is halved, the constant doubles. This counterintuitive result is reasoned clearly.

My impression of this book is that while it covers very similar material to Touger's, it expects more from the student. Most chapters have enough information for a complete first-year undergraduate module. However, in an algebra-based text such as this, some topics are simply not dealt with at the level one might wish. Resonance and damped simple harmonic motion are described conceptually, not mathematically. They are hardly mentioned by Touger.

The books by Serway and Jewett and Halliday et al are calculus-based texts.

Both are longer by some 200 pages or more and can thus go into greater depth. The Schrodinger wave equation, for example, is described by Touger in classical terms without mentioning that the kinetic energy operator is a second differential. The equation is not given, and one wonders how much students will really understand from this simplified approach. Cutnell and Johnson sensibly avoid the topic in their discussion of quantum phenomena, but both Serway and Jewett and Halliday et al deal fully with the mathematics of this important equation.

Halliday's is probably the harder of the two texts. It contains fewer diagrams than Serway and Jewett's, though there are still plenty, and relies more on visualisation and conceptual understanding. Both also make extensive use of worked examples and end-of-chapter problems, but neither book is without its flaws. For example, both place a great deal of emphasis on context, but not convincingly. Seismic waves are used in both books to introduce oscillations, but the text rapidly reverts to a traditional mass-on-a-spring approach. In addition, Halliday shows how seismic waves were used to estimate the depth of the Russian submarine Kursk, which sank after a torpedo exploded on board in 2000. These estimates placed the submarine at 85m but it was found at 115m, and the discrepancy is not explained.

These are relatively minor faults in otherwise good books. Both Serway and Jewett and Halliday et al demand more from students by way of prior understanding but are probably closer to what I would want in an undergraduate text. Halliday has clearer explanations; Serway and Jewett provide more photographs and make good use of "mental models", which are analogies that help the reader to visualise the physics, and also have conceptually challenging worked solutions. As for the books by Touger and Cutnell and Johnson, there is little to choose between them, but I think first-year university students in the UK would better appreciate the latter.

David Sands is senior lecturer in physics, Hull University.