Multivariable and Vector Calculus

What the resources cover

The page runs from the first ideas of three-dimensional space to the big integral theorems. The mind maps Unit 1 and Unit 2 start with navigating 3-space, contour diagrams, linear functions, partial derivatives, local linearity and the gradient. The map on MTH2010 Partial Derivatives reviews dot products, cross products, lines and planes first.

Further along you will find maps on cylindrical coordinates, Lagrange multipliers and integral theorems, plus notes on vector functions and vector differentiation, and a week-by-week set of notes that includes the Laplacian, harmonic functions and the Jacobian.

Where to start

1. Open the mind maps Unit 1 and Unit 2 to get the picture of functions of several variables.
2. Read the notes on vector functions and the properties of vector differentiation.
3. Take the Partial Diretives quiz and the Unit 2 test to check partial derivatives and gradients.
4. Move on to the Multiple Integrals quiz, which asks you to use polar coordinates and find areas between curves.

Using quizzes and maps together

Read a map first, then try a quiz on the same idea. If a question surprises you, go back to the branch of the map that covers it. There are short quizzes on divergence, curvature, the Laplacian, tangent planes, gradient and directional derivatives, and vector fields, so you can check one idea at a time.

Flashcards suit the formulas. The Vector Calculus flash cards deck asks about the divergence theorem, Green's Theorem, Stoke's Theorem and volume elements for cylinders and spheres. The Multivariable Calculus deck covers the line integral formula, the fundamental theorem for line integrals, curl and divergence.

Where it fits

This unit sits in the Calculus strand of Mathematics. It suits university students, and teachers can use the maps, quizzes and decks as ready-made material for a class.

Choose one map today, test yourself with a quiz, then write a few flashcards of your own for the formulas you keep forgetting.