Khan Academy: Multivariable Calculus: Position Vector Valued Functions

Video lesson defining the derivative of a position vector valued function by visualizing it and setting it up. [14:45]

Video lesson reviewing position vector valued functions and their derivatives.

Video lesson reviewing position vector valued functions and their derivatives. Explanation does not contain any specific examples. [5:04]

Video lesson defining the derivative of a position vector valued function by visualizing it and setting it up.

Video lesson solving for the derivatives for a two specific vector-valued functions that describe the same path but have different velocities. [12:45]

Video continuing to show how to parameterize a torus using two parameters by writing the position vector valued functions. [16:32]

Video finding a gradient in three dimensions by using an example about temperature in a 3-D room. Graph of the vector field found in the solution is shown. [10:54]

Video showing how to take the partial derivatives of a generalized vector-valued function by taking the partial derivative of each part of the function. Video is meant as a build-up to the videos on surface integrals. [10:07]

A more formal understanding of functions. This video introduces the term codomain and contrasts it with the term range. It also introduces the terminology scalar-valued function, real-valued function, and vector-valued function. [16:01]

Video lesson introducing gradients in two dimensions by calculating a gradient and then explaining what it is using a 3-D graph. [9:45]