Interactive Differential Equations
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main>Graphing Two-Dimensional Equations

I.

First Order Differential Equations

Labs for Part I

1. Newton's Law of Cooling

2. Graphing Differential Equations

3. Single Species Population Models

4. Falling Bodies and Golf

5. Numerical Methods

6. Isoclines and Fences

7. Existence and Uniqueness

8. Orthogonal Trajectories

II.

Second Order Differential Equations

Labs for Part II

9. Linear Oscillators: Free Response

10. Free Vibrations

11. Forced Vibrations: An Introduction

12. Forced Vibrations: Advanced Topics

13. Electrical Circuits

14. Laplace Transforms

III.

Linear Algebra

Labs for Part III

15. Linear Algebra

16. Linear Classification

IV.

Systems of Differential Equations

Labs for Part IV

17. Graphing Two-Dimensional Equations

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  Tools:  
    a. Simple Harmonic Oscillator
    b. Parametric to Cartesian
    c. Phase Plane Drawing
    d. Vector Fields
    e. Two Dimensional Equations
    f. Lotka-Volterra

18. Romeo and Juliet

19. The Glider

20. Nonlinear Oscillators: Free Response

21. Predator-Prey Population Models

22. Competing Species Population Models

V.

Chaos and Bifurcation

Labs for Part V

23. Bifurcations, 1-D

24. Spruce Budworm

25. Bifurcations in Planar Systems

26. Chaos in Forced Nonlinear Oscillators

27. The Lorenz Equations

VI.

Series Solutions and Boundary Value Problems

Labs for Part VI

28. Maclaurin Series, Airy's Series

29. Special Functions (from Series Solutions)

30. Boundary Value Problems

31. Fourier Series