Modelling Differential Equations in Biology

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C. H. TaubesCambridge University PressEdition: 2, 1/17/2008EAN 9780521708432, ISBN10: 0521708435Paperback, 526 pages, 24.6 x 17.4 x 2.4 cmLanguage: EnglishBased on a very successfu l one-semester course taught at Harvard, this text teaches students in the life sciences how to use differential equations to help their research. It needs only a semester's background in calculus. Ideas from linear algebra and partial differential equations that are most useful to the life sciences are introduced as needed, and in the context of life science applications, are drawn from real, published papers. It also teaches students how to recognize when differential equations can help focus research. A course taught with this book can replace the standard course in multivariable calculus that is more usually suited to engineers and physicists.1. Introduction2. Exponential growth with appendix on Taylor's theorem3. Introduction to differential equations4. Stability in a one component system5. Systems of first order differential equations6. Phase plane analysis7. Introduction to vectors8. Equilibrium in two component, linear systems9. Stability in non-linear systems10. Non-linear stability again11. Matrix notation12. Remarks about Australian predators13. Introduction to advection14. Diffusion equations15. Two key properties of the advection and diffusion equations16. The no trawling zone17. Separation of variables18. The diffusion equation and pattern formation19. Stability criteria20. Summary of advection and diffusion21. Traveling waves22. Traveling wave velocities23. Periodic solutions24. Fast and slow25. Estimating elapsed time26. Switches27. Testing for periodicity28. Causes of chaosExtra exercises and solutionsIndex.'Graduates of this course will be prepared to discuss the setup and structure of the underlying model, and to engage with the type of predictions that it can make. That's an admirable accomplishment for a book at this level! Moreover, equipping undergraduates with such a toolkit can open truly exciting doors for thinking about biology, a theme that runs throughout this text.' SIAM Review Show more