Mathematical Models in the Biosciences I

An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students.

“The choice of material is interesting and refreshing, and finds concrete applications for mathematical topics that might not be standard fare in the physics or chemistry curricula. The applications of the Poincaré-Bendixson theorem to locating limit cycles are a remarkable highlight.”—Chay Paterson, zbMATH Open"This is a wonderful book, wise and witty. It would have taught me most of the math I needed for my career in research – if I did all the problems."—Stephen Stearns, author of The Evolution of Life Histories and Evolutionary Medicine  “This enlightening book covers not only the essential parts of calculus and dynamical system, but also how one can apply these tools in biological sciences. In addition, the last chapter of this book is a concise introduction to probability theory. Michael Frame motivates students with very well-selected examples.”—Hongyu He, Professor of Mathematics, Louisiana State University“This work is an important step toward a new curriculum model for the nascent field of mathematical biology: different content and authentic applications, geared toward a truly interdisciplinary audience.”—Rebecca Gasper, Assistant Professor of Mathematics, Creighton University

Michael Frame retired in 2016 as adjunct professor of mathematics at Yale University. For more than twenty years Frame taught courses on fractal geometry and calculus based on applications in biology and medicine. Amelia Urry and he are the coauthors of Fractal Worlds: Grown, Built, and Imagined.