Authors:
- 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
- Includes supplementary material: sn.pub/extras
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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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Authors and Affiliations
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Departments of Medicine (Cardiology) and Integrative Biology and Physiology, University of California Los Angeles, Los Angeles, USA
Alan Garfinkel
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Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, USA
Jane Shevtsov
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Los Angeles, USA
Yina Guo
About the authors
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.
Bibliographic Information
Book Title: Modeling Life
Book Subtitle: The Mathematics of Biological Systems
Authors: Alan Garfinkel, Jane Shevtsov, Yina Guo
DOI: https://doi.org/10.1007/978-3-319-59731-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-59730-0Published: 02 October 2017
Softcover ISBN: 978-3-319-86689-5Published: 14 August 2018
eBook ISBN: 978-3-319-59731-7Published: 06 September 2017
Edition Number: 1
Number of Pages: XV, 445
Number of Illustrations: 54 b/w illustrations, 299 illustrations in colour
Topics: Mathematical and Computational Biology, Mathematical Modeling and Industrial Mathematics, Ordinary Differential Equations