Khan Academy: Calculus: Differential of a Vector Valued Function

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]

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

Video lesson reviewing position vector valued functions and their derivatives.

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

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

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 introducing surface integrals by building on the partial derivatives of vector-valued functions from the previous video and showing how to visualize a surface integral. Surface area is found by taking the magnitude of the cross...

Video that first reviews the concept of work, then gives a vector field and sets up a line integral to find the work done on a particle moving along a path using a dot product. [16:46]

Video lesson explaining position vector-valued functions by visualizing and setting one up. [7:45]