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.
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