Calculus
∫ Core Calculus
The essential sequence from limits through integration — the ideas that power all of modern science and engineering.
- 1→
Limits
The foundational idea of calculus — what a function approaches as its input gets arbitrarily close to a value.
- 2→
Lebesgue Integral
A more powerful way to integrate than Riemann's — slice the range instead of the domain, making sense of integrals that the Riemann integral can't handle.
- 3→
Derivatives
The instantaneous rate of change of a function — defined as the limit of the difference quotient and interpreted as the slope of a tangent line.
- 4→
Integrals
The integral as accumulated area — Riemann sums, definite integrals, and the antiderivative as an operation that reverses differentiation.
- 5→
Fundamental Theorem of Calculus
The bridge connecting differentiation and integration — why antiderivatives compute areas and why the two operations are inverses of each other.
- 6→
Applications of Integration
Computing areas between curves, volumes of solids of revolution, arc lengths, and other accumulated quantities.