Biology in Time and Space

A Partial Differential Equation Modeling Approach

James P. Keener

• Publisher: American Mathematical Society
• Year: 2021
• ISBN:
  9781470464141
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.This book tells the story of living processes that change in time and space. Driven by scientific inquiry, methods from partial differential equations, stochastic processes, dynamical systems, and numerical methods are brought to bear on the subject, and their exposition seems effortless in the pursuit of deeper biological understanding. With subjects ranging from spruce budworm populations to calcium dynamics and from tiger bush patterns to collective behavior, this is a must-read for anyone who is serious about modern mathematical biology.—Mark Lewis, University of AlbertaProf. Keener is one of the Great Minds in Math Biology who has trained generations of fine scientists and mathematicians over the years.—Leah Edelstein-Keshet, University of British ColumbiaThis is a fantastic book for those of us who teach mathematical modelling of spatiotemporal phenomena in biology, and for anyone who wishes to move into the field. It guides the reader on how one should tackle the art of modelling and, in a very systematic and natural way, introduces many of the necessary mathematical and computational approaches, seamlessly integrating them with the biology. It is a pleasure to read.—Philip Maini, University of OxfordMathematical Biology has few foundational texts. But this is one.—Michael C. Reed, Duke University

Table of contents

• Cover
• Title page
• Copyright
• Contents
• Preface
• Chapter 1. Background Material
• Chapter 2. Conservation— Learning How to Count
• Chapter 3. The Diffusion Equation— Derivations
• Chapter 4. Realizations of a Diffusion Process
• Chapter 5. Solutions of the Diffusion Equation
• Chapter 6. Diffusion and Reaction
• Chapter 7. The Bistable Equation—Part I: Derivations
• Chapter 8. The Bistable Equation—Part II: Analysis
• Chapter 9. Advection and Reaction
• Chapter 10. Advection with Diffusion
• Chapter 11. Chemotaxis
• Chapter 12. Spatial Patterns
• Chapter 13. Dispersal-Renewal Theory
• Chapter 14. Collective Behavior
• Appendix A. Introduction to Matlab
• Appendix B. Constants, Units, and Functions
• Appendix C. Selected Answers to Exercises
• Bibliography
• Index
• Back Cover