## Math 230 - Differential equations

**Videos for Differential Equations**

Videos provided thru MIT Open Courseware (here).

**Resources Available: **Text (2), Student
Solutions manual (2)

1:
The Geometrical View of y'=f(x,y)

2:
Euler's Numerical Method for y'=f(x,y)

3:
Solving First-order Linear ODE's

4:
First-order Substitution Methods

5:
First-order Autonomous ODE's

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 ODE's

12:
Continuation: General Theory for Inhomogeneous ODE's.

13:
Finding Particular Solutions to Inhomogeneous ODE's

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 ODE's with Discontinuous
Inputs.

23:
Use with Impulse Inputs

24:
Introduction to First-order Systems of ODE's

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 ODE's

Note: These are the subjects of some of the videos available
on the MIT website, please click on the link above to access the
videos.

Last updated: July 18, 2011