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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 I, Lecture 2 - "Arrow" Arithmetic

Herb Gross reviews the definition of vectors - objects that have magnitude, direction, and sense. He also defines equality of vectors, their components, and rules of arithmetic. Vector arithmetic shares many structural properties with scalar arithmetic including a zero and additive inverse. This video also covers the multiplication of a vector times a scalar.


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