Disc 1. Lecture 1. What is a differential equation?
Lecture 2. A limited-growth population model
Lecture 3. Classification of equilibrium points
Lecture 4. Bifurcations, drastic changes in solutions
Lecture 5. Methods for finding explicit solutions
Lecture 6. How computers solve differential equations.
Disc 2. Lecture 7. Systems of equations, a predator-prey system
Lecture 8. Second-order equations, the mass-spring system
Lecture 9. Damped and undamped harmonic oscillators
Lecture 10. Beating modes and resonance of oscillators
Lecture 11. Linear systems of differential equations
Lecture 12. An excursion into linear algebra.
Disc 3. Lecture 13. Visualizing complex and zero eigenvalues
Lecture 14. Summarizing all possible linear solutions
Lecture 15. Nonlinear systems viewed globally, nullclines
Lectures 16. Nonlinear systems near equilibria, linearization
Lecture 17. Bifurcations in a competing species model
Lecture 18. Limit cycles and oscillations in chemistry.
Disc 4. Lecture 19. All sorts of nonlinear pendulums
Lecture 20. Periodic forcing and how chaos occurs
Lecture 21. Understanding chaos and iterated functions
Lecture 22. Periods and ordering of iterated functions
Lecture 23. Chaotic itineraries in a space of all sequences
Lecture 24. Conquering chaos, Mandelbrot and Julia sets.
