Khan Academy: Calculus: Partial Derivatives of Vector Valued Functions

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

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 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 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 lesson introducing partial derivatives by showing a 3-D coordinate system and solving an example. [11:11]

Video lesson continuing an introduction to partial derivatives by looking at an example differentiated with respect to a different variable. A 3-D graph is included to help visualize the solution. Various examples without graphs are also...

Video lesson reviewing position vector valued functions and their derivatives.