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