Isotoon explains calculus by drawing the idea behind each rule. Ask what a derivative, an integral or a limit actually means and get a short animated video of the slope shrinking to a point, the area filling in or the series closing in on its limit.
Starts from a car's speedometer and a graph of distance over time, shows why an average speed misses the detail, then shrinks the gap between two points to zero until the secant line becomes the tangent line, whose slope is the derivative.
Scenes, in order:
Calculus is often taught as a list of rules to apply. Ask what a rule means and see it drawn: a slope shrinking to a point, an area filling in, a series closing in on its limit.
A derivative is an instantaneous rate of change. The average rate between two points is the slope of the secant line through them. As the second point slides toward the first, that slope approaches the slope of the tangent line, and that limit is the derivative. A car's speedometer shows the derivative of distance with respect to time: how fast the distance is changing right now.
The fundamental theorem says that integrating and differentiating undo each other. Picture the area under a curve f from a fixed starting point up to x. Nudge x forward by a tiny amount dx and the area grows by a thin strip about f(x) tall and dx wide, so the area grows at the rate f(x). That is why the area under f from a to b is F(b) − F(a) for any antiderivative F.
When one quantity depends on another that is itself changing, the rates multiply. If y changes 3 times as fast as u, and u changes 2 times as fast as x, then y changes 6 times as fast as x. For a composite function f(g(x)) that is f′(g(x)) · g′(x): the outer function's rate, taken where you are, times the inner function's rate.
The ones marked 3D become a model you can turn, step through and tap.
Every claim is checked before anything is drawn, and every video lists its sources. See plans