Applied Mathematics for Earth Scientists

Abstract

Writing an applied mathematics book can be hazardous to one's ego. First, there typically are strong and incompatible opinions on what should go into such a book, and second, there are already many excellent applied mathematics books on the market. Nevertheless, three prestigious geophysicists from Toyko University, Rikitake, Sato, and Hagiwara, have correctly identified a niche to be filled in this competitive market, and they have attempted to fill it with the publication of Applied Mathematics for Earth Sciences.A more appropriate title for this book might be “Applied Mathematics for Geophysicists”; it is at geophysicists and not at, say, stratigraphers that the book is aimed. The book is divided into Part I, Fundamentals (164 pages) and Part II, Applications (271 pages). The main subtitles of Part I are, in order, Fourier transform, Laplace transform, Heaviside operator, spectral analysis, special functions, Laplace equation, wave equation, and relaxation method. As separate books have been written on virtually all of these topics, one can correctly anticipate that the material presented here will be very condensed. The applications part consists of 10 chapters of examples that draw strongly on papers published by the authors. Seismology constitutes roughly a third of the applications part, with the remainder going to selected topics on Earth's gravity, rotation and tides, heat conduction, magnetic and electrical potentials, electromagnetic induction, and magnetohydrodynamics. Emphasis throughout the book is placed on selected analytical theory, as opposed to methods of numerical analysis.