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

Part V, Lecture 1 - Double Multiple Sums

Herb Gross teaches us how to calculate infinite double (multiple) sums (for topics in calculus of several variables). This topic is analogous to the use of infinite sums in calculus of a single variable.

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