Calculus Revisited: Multivariable Calculus

Part II: Vector Calculus

In the Single Variable Calculus course, Professor Gross discussed the calculus of a single real variable in which the domain of a function was a subset of the real numbers. Geometrically speaking, the domain of a function was a subset of the x-axis. In this part of the course, he generalizes the domain as being a subset of either the two-dimensional xy-plane and/or the three-dimensional xyz-space. Now, in the language of vectors, a function maps 2 and 3 dimensional vectors into the set of real numbers. He then uses these functions to show how we compute the velocity and acceleration of an object moving in space.

Lecture 1: Vector Functions of a Scalar Variable

Lecture 2: Tangential & Normal Vectors

Lecture 3: Polar Coordinates

Lecture 4: Vectors in Polar Coordinates