# InfoCoBuild

## Calculus Revisited: Multivariable Calculus

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 4 - The Chain Rule

Herb Gross shows examples of the chain rule for several variables and develops a proof of the chain rule. He also explains how the chain rule works with higher order partial derivatives and mixed partial derivatives.

Go to the Course Home or watch other lectures:

 Part I - Vector Arithmetic (6) Part I, Lecture 1 - The "Game" of Mathematics Part I, Lecture 2 - "Arrow" Arithmetic Part I, Lecture 3 - Three-Dimensional Vectors Part I, Lecture 4 - The Dot Product Part I, Lecture 5 - The Cross Product Part I, Lecture 6 - Equations of Lines & Planes Part II - Vector Calculus (4) Part II, Lecture 1 - Vector Functions of a Scalar Variable Part II, Lecture 2 - Tangential & Normal Vectors Part II, Lecture 3 - Polar Coordinates Part II, Lecture 4 - Vectors in Polar Coordinates Part III - Partial Derivatives (6) Part III, Lecture 1 - n-Dimensional Vector Spaces Part III, Lecture 2 - Calculus of Several Variables Part III, Lecture 3 - Directional Derivatives Part III, Lecture 4 - The Chain Rule Part III, Lecture 5 - Integrals Involving Parameters Part III, Lecture 6 - Exact Differentials Part IV - Matrix Algebra (5) Part IV, Lecture 1 - Linearity Revisited Part IV, Lecture 2 - The "Game" of Matrices Part IV, Lecture 3 - Inverting a Matrix Part IV, Lecture 4 - Inverting More General Systems of Equations Part IV, Lecture 5 - Maxima and Minima in Several Variables Part V - Multiple Integration (5) Part V, Lecture 1 - Double Multiple Sums Part V, Lecture 2 - The Fundamental Theorem Part V, Lecture 3 - Multiple Integration and the Jacobian Part V, Lecture 4 - Introduction to Line Integrals Part V, Lecture 5 - Green's Theorem