Calculus Revisited: Multivariable Calculus

Part III: Partial Derivatives

In this part, Professor Gross uses the “game of mathematics” concept to develop an analytical way to extend the domain of a function to beyond 3 dimensions. In particular, he shows how by using vector arithmetic, the rules of arithmetic that were used in developing the calculus of a single variable turn out to be the same that we use to develop the calculus of several variables. This leads to a discussion of how we replace the concept of slope in the 2 and 3-dimensional calculus by such concepts as the directional derivative when dealing with more than 3 dimensions.

Lecture 1: n-Dimensional Vector Spaces

Lecture 2: Calculus of Several Variables

Lecture 3: Directional Derivatives

Lecture 4: The Chain Rule

Lecture 5: Integrals Involving Parameters

Lecture 6: Exact Differentials