Every page in this folder names an idea you first wrestled with at the boards — in a visibly random group, marker in hand, before anyone told you what it was called. That order is deliberate: the wrestling builds the understanding, and these pages consolidate it, written for your future forgetful self. Read them after the exploration, never instead of it.
This course has two big ideas, and both deserve a moment of honest wonder. First: the instant made precise — a speed right now, not over any interval at all. Second: arrows that do algebra — quantities with direction that you can add, scale, and multiply. The pages below walk the same road the semester does.
Unit 1 — Rates of change and the limit
Unit 2 — The derivative’s toolbox
- Derivative Rules
- The Chain Rule
- Derivatives of Exponential Functions
- Derivatives of Sinusoidal Functions
- Motion on a Line
Unit 3 — What derivatives are for
Unit 4 — Vectors, lines, and planes
- What Vectors Are
- Adding and Scaling Vectors
- The Dot Product
- The Cross Product
- Equations of Lines
- Equations of Planes
- Intersections of Lines and Planes
Most pages end by pointing at the practice set that turns the idea into a reflex, and at the curriculum expectations the page serves — so you can always see where you are and why we are here.