Differential Equations

These notes are under construction

Course 18.03

Course Video Playlist

O: Unanalytic Methods

1. Geometric Methods

2. Numerical Methods

   I: First Order Differential Equations

3. First Order Linear ODE’s

4. First-order Substitution Methods: Bernouilli and Homogeneous ODE’s.

5. First-order Autonomous ODE’s: Qualitative Methods

6. Complex Numbers and Complex Exponentials

7. First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.

8. Applciation: Mixing Problem

   II: Second Order Differential Equations

9. Linear Second Order ODE Constant Coefficients

10. Application: Spring-Mass-Dashpot System

11. Theory of General Second-order Linear Homogeneous ODE’s

12. Theory for Nonhomogeneous ODE’s

13. Methods for Particular Solution

14. Application: Resonance

    III: Fourier Series and Laplace Transform

15. Introduction to Fourier Series

16. Fourier Series w/ General Periods

17. Finding Particular Solutions via Fourier Series

18. Blank

19. Introduction to Laplace Transform

20. Laplace of derivative

21. Convolution

22. Laplace Transform with jump discontinuities

23. Laplace Transform with impulse input

    IV: First Order Systems

24. Introduction to First-order Systems of ODEs

25. First-order Systems continued

26. First-order Systems w/ Repeated or Complex roots

27. Sketching for first order system

28. Theories for Nonhomogeneous Systems

29. Matrix Exponentials for complementary solutions

30. Decoupling

31. Autonomous Systems