Fourier series, from the heat equation to sines to cycles.

Fourier series, from the heat equation to sines to cycles.

Solving the heat equation.

Solving the heat equation.

In this video Paul Andersen shows conceptual thinking in a mini-lesson on boundary and initial conditions within systems.

Boundary conditions - the dividing line between system and enviro
nment
Initial condition - the...

Inventor and MacArthur fellow Saul Griffith shares some innovative ideas from his lab -- from "smart rope" to a house-sized kite for towing large loads.

From 2016 to 2019, the world saw record-breaking heat waves, rampant wildfires, and the longest run of category 5 tropical cyclones on record. The number of extreme weather events has been increasing for the last 40 years, and current...

Now that we know what differential equations are, we have to learn how to classify them. We have to know whether a DE is ordinary or partial, linear or nonlinear, homogenous or nonhomogenous, autonomous or nonautonomous. We have to be...

Now that we know how to classify differential equations, we have to learn how to solve them. Let's start with the easiest ones to solve, separable first-order differential equations. This will involve some simple algebra and then basic...

34 Buck-Boost Converter Analysis and Design | Power Electronics

33 Boost Converter Analysis and Design | Power Electronics

The 1 dimensional wave equation is solved here using the separation of variables technique (assuming u(x,t) = phi(x) q(t).



I simplify the formula further using the boundary c

onditions:


u(0,t) = 0

...