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December 27, 2022


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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.

About the Instructor

Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.


Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.

Other Resources by Herb Gross

Calculus Revisited: Single Variable Calculus

Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

Course Curriculum

    • The “Game” of Mathematics Unlimited
    • Three-Dimensional Vectors Unlimited
    • Three-Dimensional Vectors Unlimited
    • The Dot Product Unlimited
    • The Cross Product Unlimited
    • Equations of Lines & Planes Unlimited
    • Vector Functions of a Scalar Variable Unlimited
    • Tangential & Normal Vectors Unlimited
    • Polar Coordinates Unlimited
    • Vectors in Polar Coordinates Unlimited
    • n-Dimensional Vector Spaces Unlimited
    • Calculus of Several Variables Unlimited
    • Directional Derivatives Unlimited
    • The Chain Rule Unlimited
    • Integrals Involving Parameters Unlimited
    • Exact Differentials Unlimited
    • Linearity Revisited Unlimited
    • The “Game” of Matrices Unlimited
    • Inverting a Matrix Unlimited
    • Inverting More General Systems of Equations Unlimited
    • Maxima and Minima in Several Variables Unlimited
    • Double Multiple Sums Unlimited
    • The Fundamental Theorem Unlimited
    • Multiple Integration and the Jacobian Unlimited
    • Introduction to Line Integrals Unlimited
    • Green’s Theorem Unlimited

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Massachusetts Institute of Technology