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Modeling Life

The Mathematics of Biological Systems

Author(s):
Publisher:

Springer

Pages: 445
Further Actions:

Recommend to library

AVAILABLE FORMATS

Paperback - 9783319866895

14 August 2018

€57.19

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Hardcover - 9783319597300

07 September 2017

€57.19

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Ebook - 9783319597317

06 September 2017

€44.02

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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within...

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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey 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 counter-intuitive 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 early-stage 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 two-quarter 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, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

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Tackles highly relevant material across the life sciences, using tools best-suited to the field


Driven by real-world 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

1. Modeling, Change, and Simulation
2. Derivatives and Integrals
3. Equilibrium Behavior
4. Non-Equilibrium Dynamics: Oscillation
5. Chaos
6. Linear Algebra
7. Multivariable Systems
Bibliography
Index.
“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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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...

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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.

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