Calculus

Secants collapse onto tangents: the difference quotient, the derivative function, the power rule, and the four library derivatives.

Product, quotient, and chain rules; combining them, and second derivatives — the whole differentiable world unlocked.

Tangent and normal lines, rise and fall, peaks and valleys certified two ways, concavity — and optimization, the art of the best.

Differentiation reversed, areas by slicing, and the Fundamental Theorem that collapses infinite sums into one subtraction.

Areas between curves, motion recovered from velocity, average values — and a capstone running the whole course in one arc.