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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 V, Lecture 3 - Multiple Integration and the Jacobian

Herb Gross illustrates how the Jacobian arises when changing coordinates in order to calculate a double integral.

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