Calculus The mathematics of change, from zero: limits and continuity, the derivative and every rule that computes it, curve-sketching and optimization, then integrals, the Fundamental Theorem, and what areas can do. Secants collapse onto tangents and staircases melt into exact areas — every big idea arrives as a moving picture.
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The course — 6 units, in order
01 Limits & Continuity What a function is heading toward: limits from graphs and algebra, limits at infinity, and the definition of an unbroken graph. Start 02 The Derivative Secants collapse onto tangents: the difference quotient, the derivative function, the power rule, and the four library derivatives. Start 03 Differentiation Techniques Product, quotient, and chain rules; combining them, and second derivatives — the whole differentiable world unlocked. Start 04 Applications of Derivatives Tangent and normal lines, rise and fall, peaks and valleys certified two ways, concavity — and optimization, the art of the best. Start 05 Integrals Differentiation reversed, areas by slicing, and the Fundamental Theorem that collapses infinite sums into one subtraction. Start 06 Applications of Integrals Areas between curves, motion recovered from velocity, average values — and a capstone running the whole course in one arc. Start