MIT OCW - Mathematics -Differential Equations

1. The Geometrical View of y'=f(x,y)
2. Euler's Numerical Method
3. Solving First-order Linear ODEs
4. First-order Substitution Methods
5. First-order Autonomous ODEs
6. Complex Numbers and Complex Exponentials
7. First-order Linear with Constant Coefficients
8. Continuation
9. Solving Second-order Linear ODE's with Constant Coefficients
10. Continuation, Complex Characteristic Roots
11. Theory of General Second-order Linear Homogeneous ODEs
12. Continuation, General Theory for Inhomogeneous ODEs
13. Finding Particular Sto Inhomogeneous ODEs
14. Interpretation of the Exceptional Case Resonance
15. Introduction to Fourier Series
16. Continuation, More General Periods
17. Finding Particular Solutions via Fourier Series
19. Introduction to the Laplace Transform
20. Derivative Formulas
21. Convolution Formula
22. Using Laplace Transform to Solve ODEs with Discontinuous Inputs
23. Use with Impulse Inputs
24. Introduction to First-order Systems of ODEs
25. Homogeneous Linear Systems with Constant Coefficients
26. Continuation, Repeated Real Eigenvalues
27. Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
28. Matrix Methods for Inhomogeneous Systems
29. Matrix Exponentials
30. Decoupling Linear Systems with Constant Coefficients
31. Non-linear Autonomous Systems
32. Limit Cycles
33. Relation Between Non-linear Systems and First-order ODEs

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