Modeling differential equations in biology
著者
書誌事項
Modeling differential equations in biology
Prentice Hall, c2001
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内容説明・目次
内容説明
For undergraduate courses in math modeling, and biology calculus courses in departments of math and life sciences.
Designed for students who understand the simple basics of calculus, this text focuses on the differential equations and related subjects that are commonly used today by working life scientists. It emphasizes both the mathematics and how the mathematics is employed in order to introduce some potentially useful tools and modes of thought to future experimental biologists.
目次
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.
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