An interactive knowledge map
Calculus × Computing
All of university calculus and where every idea lands in AI, graphics, simulation, robotics and scientific computing. Behind this text, four of those ideas at work on a single curve: the slope, the area, the approximation and the way downhill.
Derivative: the slope of the tangent, the limit of ever-shorter secants. Computers take millions of them a second. Used in: Automatic differentiation · Physics engines
Definite integral: add up thinner and thinner rectangles and the sum closes in on the exact area. Most integrals in computing are never solved, only approximated like this. Used in: The rendering equation · Monte Carlo methods
Taylor polynomial: near a point, a polynomial built from the derivatives there hugs the curve, and each extra degree hugs it further out. The idea behind how a machine that only adds and multiplies computes sin x. Used in: Floating point (IEEE 754) · Physics engines
Gradient descent: step against the slope, x ← x − η f′(x), until the ground is flat. Where you start decides which valley you end in. Used in: Neural networks · Backpropagation