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Modeling Life

The Mathematics of Biological Systems

Authors: Garfinkel, Alan, Shevtsov, Jane, Guo, Yina

  • 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
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Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-59731-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 55,11 €
price for Spain (gross)
  • ISBN 978-3-319-59730-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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 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?

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.

Table of contents (7 chapters)

  • Modeling, Change, and Simulation

    Garfinkel, Alan (et al.)

    Pages 1-68

    Preview Buy Chapter 30,19 €
  • Derivatives and Integrals

    Garfinkel, Alan (et al.)

    Pages 69-113

    Preview Buy Chapter 30,19 €
  • Equilibrium Behavior

    Garfinkel, Alan (et al.)

    Pages 115-170

    Preview Buy Chapter 30,19 €
  • Nonequilibrium Dynamics: Oscillation

    Garfinkel, Alan (et al.)

    Pages 171-222

    Preview Buy Chapter 30,19 €
  • Chaos

    Garfinkel, Alan (et al.)

    Pages 223-271

    Preview Buy Chapter 30,19 €

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-59731-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 55,11 €
price for Spain (gross)
  • ISBN 978-3-319-59730-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Modeling Life
Book Subtitle
The Mathematics of Biological Systems
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-59731-7
DOI
10.1007/978-3-319-59731-7
Hardcover ISBN
978-3-319-59730-0
Edition Number
1
Number of Pages
XV, 445
Number of Illustrations and Tables
54 b/w illustrations, 299 illustrations in colour
Topics