# 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 6 - Exact Differentials

Herb Gross explains the necessary and sufficient condition for an expression of the form Mdx + Ndy to be an exact differential.

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