Multivariable Calculus

9 units · licensed

Calculus III: vectors and space, functions of several variables, and integration over regions, curves and fields.

Unit 1

Vectors in space

Dot and cross products, magnitude, angle and projection

0% mastery

Start

Unit 2

Lines, planes and surfaces

Plane equations, distances and quadric traces

0% mastery

Start

Unit 3

Vector-valued functions

Velocity, speed, arc length and curvature

0% mastery

Start

Unit 4

Partial derivatives

First and second partials, including mixed

0% mastery

Start

Unit 5

Gradients and directional derivatives

The chain rule for several variables, gradients and rates in a direction

0% mastery

Start

Unit 6

Optimisation of several variables

Critical points, the second derivative test and Lagrange multipliers

0% mastery

Start

Unit 7

Double integrals

Iterated integrals, order of integration and polar regions

0% mastery

Start

Unit 8

Triple integrals

Volumes in rectangular, cylindrical and spherical coordinates

0% mastery

Start

Unit 9

Vector fields and line integrals

Work, conservative fields, potential functions and Green's theorem

0% mastery

Start

Loop practice

Cycle through all 9 units until you get 180 right (20 × 9 units).

Mastery saved per unit

Start