Calculus
Each Big Idea is one episode for everyone. Its Deep Dives follow it, for a student taking the course.
Big Idea 1The Derivative: Nobody Measured Usain Bolt's Top SpeedSpeed at one moment is the slope you get when you zoom in until the curve looks straight. That slope is the derivative.
Deep Dive 1.1The Limit: Is the Slope 6, or Nothing?The derivative isn't the slope of any chord; it's the number the chord slopes head for, found by doing the algebra while the gap is still not zero.
Deep Dive 1.2The Power Rule: Why the Power Comes DownMultiply out the rise, (x + h)ⁿ − xⁿ, and every term but one carries an extra h; the limit keeps only n·xⁿ⁻¹.
