Learning path · Mathematics
Calculus Foundations
Build the language of change and accumulation from functions through integration.
- 01Orientation→
Functions: Machines, Maps, and Relationships
Why a function is more than a formula—and how it organizes dependence throughout mathematics and science.
- 02Foundations→
Why Limits Matter
The quiet idea that makes continuity, derivatives, and integrals possible.
Requires: Functions: Machines, Maps, and Relationships
- 03Core Concepts→
Continuity: When Nearby Inputs Stay Nearby
A precise account of what it means for a function to have no break at a point.
Requires: Why Limits Matter
- 04Core Concepts→
Derivatives Measure Local Change
How one limit turns average change into slope, velocity, and sensitivity at a single point.
Requires: Why Limits Matter
- 05Core Concepts→
Integrals Turn Rates into Accumulation
Build the definite integral from finite sums, interpret its units and sign, and connect accumulation to antiderivatives.
Requires: Derivatives Measure Local Change · Summation Notation Makes Repeated Addition Precise