Modeling Differential Equations in Biology
Autor Clifford Henry Taubesen Limba Engleză Paperback – 16 ian 2008
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Specificații
ISBN-13: 9780521708432
ISBN-10: 0521708435
Pagini: 526
Ilustrații: 81 b/w illus. 120 exercises
Dimensiuni: 174 x 246 x 24 mm
Greutate: 1.03 kg
Ediția:2
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom
ISBN-10: 0521708435
Pagini: 526
Ilustrații: 81 b/w illus. 120 exercises
Dimensiuni: 174 x 246 x 24 mm
Greutate: 1.03 kg
Ediția:2
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom
Cuprins
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.
Recenzii
'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
Descriere
Aimed at biologists wishing to understand mathematical modelling rather than just learning mathematical methods.