Modeling Life
The Mathematics of Biological Systems
Authors: Garfinkel, Alan, Shevtsov, Jane, Guo, Yina
Free Preview Tackles highly relevant material across the life sciences, using tools bestsuited to the field
 Driven by realworld examples drawn from biology, ecology, medicine, and beyond
 Builds effective mathematical modeling skills from beginning to end
 Illustrates every step with engaging, informative graphics in full color
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 About this Textbook

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predatorprey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counterintuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions.
Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of earlystage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking.Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a twoquarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, realworld framework. In all cases, the focus is clear: how does the math help us understand the science?
 About the authors

Alan Garfinkel received his undergraduate degree from Cornell in Mathematics and Philosophy,and a PhD from Harvard in Philosophy and Mathematics. After some years of practicing philosophy of science, Garfinkel transitioned to medical research, applying qualitative dynamics to phenomena in medicine and physiology. Along with James Weiss and Zhilin Qu, he studies cardiac arrhythmias from the point of view of nonlinear dynamics.
Jane Shevtsov earned her BS in Ecology, Behavior and Evolution from UCLA, and her PhD in Ecology from the University of Georgia. Her main research interests lie in mathematical models of food webs and ecosystems.
Yina Guo received her PhD from Nankai University in Control Engineering. Her PhD thesis used partial differential equations to explain the branching structure of the lung. Her computer simulations of branching processes were featured on the cover of the Journal of Physiology. She is particularly interested in the use of graphics and visualization techniques in both research and teaching.  Reviews

“The book can serve as an introduction to the field of modeling not only for university students but for any person interested in the field with little or no knowledge of calculus. … This book is a very interesting deviation from this prevailing paradigm. It takes the essence of calculus and presents it in a way which is accessible and usable in the practice of life sciences professionals.” (Svetoslav Markov, zbMATH 1397.92001, 2018)
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 Table of contents (7 chapters)


Modeling, Change, and Simulation
Pages 168

Derivatives and Integrals
Pages 69113

Equilibrium Behavior
Pages 115170

Nonequilibrium Dynamics: Oscillation
Pages 171222

Chaos
Pages 223271

Table of contents (7 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Modeling Life
 Book Subtitle
 The Mathematics of Biological Systems
 Authors

 Alan Garfinkel
 Jane Shevtsov
 Yina Guo
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG
 eBook ISBN
 9783319597317
 DOI
 10.1007/9783319597317
 Hardcover ISBN
 9783319597300
 Softcover ISBN
 9783319866895
 Edition Number
 1
 Number of Pages
 XV, 445
 Number of Illustrations
 54 b/w illustrations, 299 illustrations in colour
 Topics