Multivariable Calculus — Vectors & Gradients
Vectors (dot, cross, length), functions of two variables, partial derivatives, and the gradient that points uphill.
Single-variable calculus lived on a line. The real world has width, depth, and height — so calculus grows extra variables. This course meets vectors and the partial derivative, the engine behind 3-D graphics, physics, and machine learning.
- 01 Vectors in space ELI5: a vector is an arrow — it has a direction and a length. Add two by laying them tip-to-tail; scale one by stretching it. Two products matter: the dot…
- 02 Functions of two variables ELI5: a function like f(x, y) = x² + y² is a landscape — give it a spot (x, y) and it returns a height. (Its graph is a bowl.) We can't draw the 3-D…
- 03 Partial derivatives & the gradient ELI5: a partial derivative wiggles one variable while holding the others still — the slope in just that direction. We measure them numerically below. Bundle…
- 04 Finding a minimum ELI5: a low point of a landscape is flat in every direction — all partial derivatives are zero. The bowl f(x, y) = x² + y² bottoms out at the origin (0, 0),…
next course: Proofs & Logic — How We Know →