Calculus
Limits, derivatives, and integrals: the mathematics of change and accumulation, built from the ground up.
What calculus is
The two big ideas (instantaneous change and accumulation) and why they turn out to be two sides of one coin.
Limits
The idea of a value a function approaches, one-sided limits, and what it means for a function to be continuous.
The derivative
The instantaneous rate of change as the slope of a tangent line, defined as a limit of difference quotients.
Rules of differentiation
The power, constant, sum, product, quotient, and chain rules: the toolkit for differentiating without limits each time.
The integral
Antiderivatives, the definite integral as the area under a curve, and Riemann sums as the limit that defines it.
The Fundamental Theorem of Calculus
Why differentiation and integration are inverse operations, and how that lets you evaluate an area with an antiderivative.