Modeling Differential Equations in Biology

by Clifford Henry Taubes

Overview

Given that a college level life science student will take only one additional calculus course after learning its very basics, what material should such a course cover? This book answers that question. It is based on a very successful one-semester course taught at Harvard and aims to teach students in the life sciences understanding the use of differential equations. It is enriched with illustrative examples from real papers. Necessary notions from linear algebra and partial differential equations are introduced as and when needed, and in the context of applications. Drawing on a very successful one-semester course at Harvard, this text aims to teach students in the life sciences how to use differential equations. It is enriched with illustrative examples from real papers. Necessary notions from mathematics are introduced as and when needed, and in the context of applications. Aimed at biologists wishing to understand mathematical modelling rather than just learning math methods.

Product Details

ISBN-13:	9780521708432
Publisher:	Cambridge University Press
Publication date:	01/17/2008
Edition description:	New Edition
Pages:	526
Product dimensions:	6.85(w) x 9.69(h) x 0.94(d)

Table of Contents

1. Introduction; 2. Exponential growth with appendix on Taylor's theorem; 3. Introduction to differential equations; 4. Stability in a one component system; 5. Systems of first order differential equations; 6. Phase plane analysis; 7. Introduction to vectors; 8. Equilibrium in two component, linear systems; 9. Stability in non-linear systems; 10. Non-linear stability again; 11. Matrix notation; 12. Remarks about Australian predators; 13. Introduction to advection; 14. Diffusion equations; 15. Two key properties of the advection and diffusion equations; 16. The no trawling zone; 17. Separation of variables; 18. The diffusion equation and pattern formation; 19. Stability criteria; 20. Summary of advection and diffusion; 21. Traveling waves; 22. Traveling wave velocities; 23. Periodic solutions; 24. Fast and slow; 25. Estimating elapsed time; 26. Switches; 27. Testing for periodicity; 28. Causes of chaos; Extra exercises and solutions; Index.

Editorial Reviews

"The authors treatment of the mathematics itself shows a first-rate mathematician's taste and judgment combined with a genuine sympathy for the presumed capabilities and real needs of his target audience. ...Recommended."
Choice

"This book, well described by its title, stands out among the many similar books on the same subject matter by the inclusion, at the end of chapters, of quite a number of brief journal articles from the research literature which support and amplify the topics under discussion. Overall, I think the exposition is excellent; a student can learn a great deal from this book."
Hal Leslie Smith, Mathematical Reviews

From the Publisher

Taubes (mathematics, Harvard), including an article from current biology research literature as the source reading for each chapter, has created a hands-on text on using math in the biological sciences designed for students who have had calculus. Initial chapters cover the basics of ordinary differential equations with a single time derivative, focusing on equations with one and two unknowns, and considering phase plane analysis, equilibria, and stability. He then introduces partial differential equations, especially diffusion and advection equations, with additional chapters on traveling wave velocities, periodic solutions, fast and slow, estimating elapsed time, switches, testing for periodicity, and causes of chaos. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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