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Physical oceanography, a mathematical introduction with MATLAB, by Reza Malek-Madani

In about 440 pages, the book introduces the reader to the computer language MATLAB, to fundamental mathematical concepts in algebra, calculus and differential equations, to general and geophysical fluid dynamics, and finally to some concepts in physical oceanography, mainly from the field of ocean circulation modeling. In the preface, the author emphasises that the book is intended for advanced undergraduates who have already completed their elementary mathematics classes and who would like to review, and also expand, their knowledge and capabilities in mathematics with respect to physical oceanography as the final field of application. Since applied mathematics today is largely based on computer tools, the widespread language MATLAB is chosen as the working tool throughout the text. The author stresses that the approach chosen is not exhaustive, neither with respect to mathematics, nor with respect to topics from oceanography. The goal of the text rather is to motivate readers and students to evolve towards independent reading of original literature and to start their own research. For that purpose, the book contains the following chapters: first about 40 pages are devoted to MATLAB, then about 80 pages introduce or review fundamental concepts of algebra and calculus. Then about 90 pages deal with ordinary differential equations, to be followed by 70 pages on the equations of fluid dynamics and 60 pages on geophysical fluid dynamics and shallow water equations. Finally, about 80 pages cover some classical equations and solutions for ocean circulations, such as Stommel and Munk models. A 10 page outlook on today’s questions closes the presentation. Before reading the book, I was somewhat surprised about the balance of topics involved. Obviously, the majority of the text is on mathematics and fluid dynamics, rather than physical oceanography. After reading I did, however, grasp the author’s intentions and could identify the book’s merits. The text is written very nicely, and reading through the book is enjoyable. Strolling along all the fundamental concepts of undergraduate mathematics, the author manages not only to review the topics, but also to bring them into the contexts of numerical analysis and questions from the field of oceanography. All chapters include a large number of well posed problems, and on top of those there are proposals for student or learners projects that may well strengthen the freshly reviewed or acquired knowledge. In classroom work, the book should thus be well suited for a teaching environment based on reading assignments and student projects, which may even involve reading recent research papers. For self-study, the