Modeling differential equations in biology.

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.