Lowrie's book is essentially a geophysicist's ‘guidebook’ of solutions to the ‘classic’ problems in solid earth geophysics. The book presents step-by-step derivations of the most important governing equations that geophysicists use to describe the physics of the Earth. Many of the solutions presented were first realized in previous centuries by the type of great geophysicists for whom parameters are named. The topics covered include gravitation and gravity (including Earth's figure and geoid), the tides, Earth's rotation, Earth's heat, geomagnetism, and the fundamentals of seismology. Solutions are presented in a clear and thorough manner, starting from first principles.

Lowrie's book serves as a basic resource for anyone who needs to revisit the basic theory of classical geophysics. Students of geophysics – primarily advanced undergraduates and graduate students – will clearly benefit, because this book provides derivations for the governing equations that are often presented alone in more standard textbooks. In fact, Lowrie wrote a prominent geophysics textbook Fundamentals of Geophysics (Lowrie, Reference Lowrie2007) that covers the same basic topics using a different, and yet complementary, approach. While the Fundamentals textbook discusses the geological ramifications and historical context of the geophysical equations, this Equations guidebook largely replaces this narrative in favour of full derivations. Thus, students who want to expand upon these solutions, who use numerical codes that are based on them, or who simply want to know how to obtain them, will find Geophysical Equations extremely useful. Although it possible to compile these derivations from original sources, more advanced texts, or others’ lecture notes, anyone who has attempted this (for example, in the preparation of lecture notes) soon finds that clear and concise solutions can be difficult to assemble from readily available sources. This book makes this significantly easier, and thus will find an audience from instructors as well as the students referenced in its title. I wish this book had been available when I was preparing my own set of geophysics lecture notes!

Each solution starts with a brief discussion of the basic physics of a problem and an outline of the first principles needed to solve it. Even the relevant mathematical background is included (vector calculus and linear algebra; there is even a nice discussion of spherical harmonics). This introduction is followed, in a self-contained way, by all the steps and diagrams needed to obtain the important geophysical equations. Note that many ‘applications’ of these geophysical equations are left untreated. Thus, many geodynamics problems such as plate rotations on a sphere, viscous convection, postglacial rebound, and elastic plate bending, are omitted despite the fact that the continuum mechanics framework needed to solve these problems is already developed to introduce seismology. Nevertheless, the ‘fundamental’ geophysical equations are presented here in an informative and intuitive way, which makes this relatively inexpensive book an excellent investment for any geophysicist's library.