Title: Modeling differential equations in biology /
Authors: Taubes, Clifford, 1954-
Publisher: Cambridge University Press,
Year: 2008
Subjects: Differential equations.; Biology Mathematical models; Biomathematics
Abstract: "Given that a college-level life science student will take only one additional calculus course after learning the very basics of differentiation and integration, 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 how to use differential equations to facilitate their research. It requires only a semester's background in calculus. Notions from linear algebra and partial differential equations that are most useful to the life sciences are introduced as and when needed, and in the context of life science applications are drawn from real published papers. In addition, the course is designed to teach students how to recognize when differential equations can help focus research. A course taught with this book can replace a standard course in multivariable calculus that is typically taught to engineers and physicists."--Jacket.
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.