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Based on a very successful 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. 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.
'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