The book is meant for undergraduates in the life sciences who only have one semester of calculus as background. It is therefore appropriate that the book starts with a very long and gentle introduction. Systems of linear differential equations are not discussed until chapter five.
The style and concept of the book is markedly different from the usual textbooks on differential equations that are written for an engineering audience. The chapters are shorter, new material is introduced at a slower pace, and there are very few textbook-like examples focusing on theoretical aspects. There are almost no proofs. There are, on the other hand, real-life examples and actual research papers in each chapter.
The most significant difference, however, is that there are very few exercises (probably less than five per chapter). This reviewer thinks that students learning from this book will be able to understand research papers using the notions explained here if they do not differ from the examples covered in this book by too much, but that is how far their knowledge will go. They will not be able to apply their knowledge in different circumstances because they will simply not have enough practice in using these concepts, methods and notions on their own.
The back cover of the book says that the book is based on a very successful one-semester course at Harvard University. This reviewer does not doubt that there could be specific circumstances in which this textbook is the right choice, so if you think yours might be one of those circumstances, certainly take a look at this book. From time to time, however, you will need to check that your students can apply these techniques, not just understand when others use them.
Miklós Bóna is Associate Professor of Mathematics at the University of Florida.
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.