Modeling differential equations in biology / Clifford Henry Taubes.

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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 us...

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Bibliographic Details
Main Author: Taubes, Clifford, 1954- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2008.
Edition:Second edition.
Subjects:
Differential equations.
Biology > Mathematical models.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xxiii, 500 pages) : digital, PDF file(s).
Format: Electronic eBook
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.