Learn Differential Equations: Up Close with Gilbert Strang and Cleve Mole‪r‬ MIT

Gilbert Strang and Cleve Moler provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.

Differential equations connect the slope of a graph to its height. Slope = height, slope = -height, slope = 2t times height: all linear. Slope = (height)^2 is nonlinear.

The sum rule, product rule, and chain rule produce new derivatives from known derivatives. The Fundamental Theorem of Calculus says that the integral inverts the derivative.

For a linear equation with exponential input from outside and exponential growth from inside, the solution is a combination of two exponentials.

A linear equation with oscillating input has an oscillating output with the same frequency (and a phase shift).

To solve a linear first order equation, multiply each input by its growth factor and integrate those outputs.