Mathematical Models in the Applied Sciences

by A.C. Fowler, D.G. Crighton (Editor), Mark J. Ablowitz (Editor)

This book presents a thorough grounding in the techniques of modeling, and proceeds to explore a range of continuum models from an impressive array of disciplines, including biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. It assumes only a basic mathematical grounding in calculus and analysis and will provide a wealth of examples for students of mathematics, engineering, and the range of applied sciences.

418 pages, Hardcover

First published November 28, 1997

Reviews

[Tomáš Ševček · Rating 4 out of 5]

The book provides a great exposition on how real-world models are analyzed, primarily focusing on models from biology, chemistry and physics. The models are first derived from underlying natural laws or briefly explained. Nondimensionalization and scale analysis are then applied, with the resulting models being further analyzed either by means of asymptotics and perturbation methods and/or by means of the theory of ODEs, PDEs and dynamical systems. Sometimes (albeit not often), these methods are compared with numerical analysis.
The first two parts introduce asymptotic analysis and perturbation methods. However, I recommend reading a complementary book on that topic (such as the one by Bender and Orszag) simultaneously or even beforehand as the material is in my opinion not explained clearly. Moreover, the text is sprinkled with numerous typos and errors (not all of them can be found in the errata), further making the material more difficult to comprehend. Each chapter contains a set of exercises, but some of them pose quite a challenge (the author himself states that some are at the research level). Nevertheless, the book is definitely worth a read if you are interested in mathematical modeling of natural and engineering phenomena and already have some familiarity with the topic.