Khan Academy: 3 D Vector Fields, Introduction

What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...

Bring it all to three dimensions. The short video points out that the discussion in the previous presentations in two dimensions also holds true for three dimensions. The sixth video in the series of 15 specifically makes the...

See an example of how you can start to understand how the formula for a three-dimensional vector field relates to the way it looks.

Intuition behind the Divergence Theorem in three dimensions.

Continuing the intuition for how three-dimensional curl represents rotation in three-dimensional fluid flow.

This finishes the demonstration of how to compute three-dimensional curl using a certain determinant.

How to compute a three-dimensional curl, imagined as a cross product of sorts.

A worked example of a three-dimensional curl computation.

Here we start transitioning from the understanding of two-dimensional curl into an understanding of three-dimensional curl.

A description of how vector fields relate to fluid rotation, laying the intuition for what the operation of curl represents.