Mathematical Models in the Biosciences I

Michael Frame

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English

Yale University Press
10 August 2021

Biomedical engineering; Applied mathematics; Biology, life sciences; Biotechnology

This book introduces mathematical modeling to bioscience students, with first semester calculus as the only prerequisite. It is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers the essential ideas and theories of basic calculus while providing examples of how they relate and are applicable to subjects such as chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, nerve impulses, and more. He presents Pearl’s causality calculus to resolve Simpson’s paradox, simple cardiac dynamics models, basic epidemiological models including Ronald Ross’s study of malaria and its epidemic curves, and limit cycles for the glycolysis model. Based on the author’s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.

By: Michael Frame
Imprint: Yale University Press
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm, Spine: 38mm
Weight: 680g
ISBN: 9780300228311
ISBN 10: 0300228317
Pages: 544
Publication Date: 10 August 2021
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Mathematical Models in the Biosciences I

"“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"