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Modeling Differential Equations in Biology

2nd Edition

£47.99

  • Date Published: January 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521708432

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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.

    • Brought alive by reprints of recent research summary articles from Science and Nature illustrating the mathematics and demonstrating to students how the mathematics in the text is used by working biologists
    • Commentary for each reprinted article summarizes the underlying biological issues so neither students nor instructors need prior knowledge, and shows where and how the mathematics is used
    • Provides students with the mathematics that is commonly used by biologists and life scientists as opposed to the mathematics of physicists and engineers commonly found in other texts
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    Reviews & endorsements

    '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

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    Product details

    • Edition: 2nd Edition
    • Date Published: January 2008
    • format: Paperback
    • isbn: 9780521708432
    • length: 526 pages
    • dimensions: 246 x 174 x 24 mm
    • weight: 0.9kg
    • contains: 81 b/w illus. 120 exercises
    • availability: Available
  • Table of 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
    Extra exercises and solutions
    Index.

  • Instructors have used or reviewed this title for the following courses

    • Biological Math
    • Differential Equations & the Sciences
    • Modeling Biological Systems with Differential Equations
  • Author

    Clifford Henry Taubes, Harvard University, Massachusetts

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