Introduction to Mathematical Modeling and Computer Simulations /

In the classroom, mathematical modeling means lessons in problem solving, specifically problems from outside mathematics. Mastery requires mathematical knowledge and skill, surely, but also aptitudes typical textbooks don't cultivate: applications domain savvy, curatorial instinct for the most relevant mathematics, and deftness with interdisciplinary translation. Applicable mathematics potentially comes in any flavor, but mostly as a combination of the subjects surveyed in this text: calculus (single-variable and vector), linear algebra, stochastics, and ordinary and partial differential equations. This slender volume potentially supplements or synopsizes more comprehensive treatments of those topics; it compares to those testaments like a collection of folksy wisdom tales, full of parables and principles ("It is forbidden to add camels to tractors. But it is possible to multiply them"). The authors emphasize that computation conjures models to life, but demands critical caution and not just coding chops (this book utilizes Mathematica). Two complaints: exercises do reinforce elements of mathematical technique, but often they miss the mission of the book by failing to truly challenge the student to model; finally, the publisher could have copyedited more thoroughly to bring the authors' second-language English up to the standard of polished, professional prose. Summing Up: Recommended. With reservations. Undergraduates and graduate students. --David V. Feldman, University of New Hampshire