Calculus Revisited: Multivariable Calculus (Res.18-007, MIT OCW). This consists of 26 video lectures taught by
Professor Herbert Gross, on a study of the calculus of functions of several variables (vector arithmetic and vector calculus).
Calculus Revisited is a series of videos and related resources that covers the materials normally found in
freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series,
consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way
for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for
the first time. (from ocw.mit.edu)
Part III, Lecture 2 - Calculus of Several Variables
Herb Gross introduces us to the traditional Calculus of Several Variables. He defines and explains the properties of partial derivatives and shows how to draw a graph of a function of several variables. He finds the normal vector (using the cross product) and the tangent plane at a point in terms of partial derivatives. Finally, Prof. Gross shows the change of a function w in the tangent plane as an approximation to the differential of w.