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M04 · Calculus I: Single Variable

A free, illustrated L1 course of 10 modules in the Mathematics track. Modules include: Limits and continuity; The derivative as slope and rate; Differentiation rules and the chain rule.

M04 L1 · Core 10 modules · about 40 lessons 10 of 10 modules live

Part of the Mathematics track. Ships in Ring 1 (Foundation) of the roadmap.

Modules

1. Limits and continuity Live · 4 lessons
2. The derivative as slope and rate Live · 4 lessons
3. Differentiation rules and the chain rule Live · 4 lessons
4. Optimization in one dimension Live · 4 lessons
5. Integrals as accumulated area Live · 4 lessons
6. The fundamental theorem of calculus Live · 4 lessons
7. Integration techniques Live · 4 lessons
8. Sequences, series and Taylor approximation Live · 4 lessons
9. Differential equations, a first look Live · 4 lessons
10. Partial derivatives, a first look Live · 4 lessons

Signature illustrations

The pictures a learner should still see in their head a year later:

Secant line sliding to tangent, Riemann sums refining, Taylor polynomials building up, chain rule as gear ratios, a surface sliced along each input to show its two partial derivatives.

Status

10 of 10 modules are written and live. The rest follow in Ring 1.

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.