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.
Aimed at biologists wishing to understand mathematical modelling rather than just learning mathematical methods.
'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
"The authors treatment of the mathematics itself shows a first-rate mathematician's taste and judgment combined with a genuine sympathy for the presumed capabilities and real needs of his target audience. ...Recommended." Choice
"This book, well described by its title, stands out among the many similar books on the same subject matter by the inclusion, at the end of chapters, of quite a number of brief journal articles from the research literature which support and amplify the topics under discussion. Overall, I think the exposition is excellent; a student can learn a great deal from this book." Hal Leslie Smith, Mathematical Reviews