This is a beta course, so its structure, chapters, and examples may continue to change.
Differential Calculus
- Build intuition for derivatives as both limits of average rates and slopes of tangents.
- Use linear approximation to turn hard nonlinear problems into easy local estimates.
- Locate extrema and understand how monotonicity, concavity, and inflection points interact.
- Connect theory with practice: optimization, error estimation, and modeling show up throughout.
Great math is learned twice: first roughly, then precisely. Skim once for the big picture, then revisit for the proofs and details.
Symbols Used in This Article
| Symbol | Type | Pronunciation/Explanation | Meaning in This Article |
|---|---|---|---|
| Mathematical symbol | “f prime of x” | The derivative of the function at the point (the slope of the tangent line) | |
| Mathematical symbol | Delta x | The change in the independent variable, used for the average rate of change |
The derivative is the rate of change itself, and everything calculus can do rests on it. This course answers two preliminary questions first: what a derivative actually is — the limit of a difference quotient, not the intuition of a slope — and what it means, geometrically the slope of the tangent and physically the instantaneous rate of change. It then shows how to compute one: the basic rules, the chain rule, implicit, parametric, and inverse differentiation, together with the global constraints the mean value theorems impose. From there it turns to what derivatives let you do — extrema, maxima and minima, monotonicity, concavity, tangents and normals — and closes by drawing the line between a differential and a derivative.