This book was written explicitly for students of applied mathematics who want to learn more about mathematical applications in biology and physiology. It is addressed to the “mathematically sophisticated”. In practice this means that the reader needs some multivariable calculus and basic linear algebra, but mostly needs to be comfortable working with ordinary and partial differential equations.
The topics include a slightly quirky combination of standard topics and more unusual ones. The author made a clear choice to limit his scope to a few topics, and his interests dictated the general direction. About one-third of the book is devoted to topics in physiology, and two-thirds to a variety of other loosely related subjects in mathematical biology.
The first two-thirds of the book range from dimensional analysis to biogeography and epidemiology, passing through diffusion processes in biology, population dynamics, epidemiology and pharmacokinetics along the way. The first chapter, on dimensional analysis, is the weakest of all. It lacks for good examples, and in its main theorem (Buckingham’s Π Theorem), neither of the primary terms is defined. But it does get better after that. All the other chapters are clearly written introductions to specific aspects of mathematical biology with good examples.
The most unusual subject, and perhaps the most interesting, in the first two-thirds of the book is biogeography. This is primarily involves determining of the maximum number of species on an island. The isolation of islands makes them simpler to study, and hypotheses about evolutionary processes in particular are easier to evaluate.
The last one-third focuses on physiology, but really only on two aspects. The first is biological fluid dynamics and the second is physiology of the heart. The relevant equations of fluid dynamics are stated but not derived, and the applications are largely to arterial blood flow. The discussion of heart physiology is limited to two specific topics: the mechanics of the left ventricle and heart valve vibration.
Without any attempt to address the subject comprehensively, the author has managed to select topics that span a considerable range across mathematical biology. Students who use the book will get a corresponding broad exposure.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.