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September 23, 2023


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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)

Course Curriculum

    • Part I, Lecture 1 – The “Game” of Mathematics Unlimited
    • Part I, Lecture 2 – “Arrow” Arithmetic Unlimited
    • Part I, Lecture 3 – Three-Dimensional Vectors Unlimited
    • Part I, Lecture 4 – The Dot Product Unlimited
    • Part I, Lecture 5 – The Cross Product Unlimited
    • Part I, Lecture 6 – Equations of Lines & Planes Unlimited
    • Part II, Lecture 1 – Vector Functions of a Scalar Variable Unlimited
    • Part II, Lecture 2 – Tangential & Normal Vectors Unlimited
    • Part II, Lecture 3 – Polar Coordinates Unlimited
    • Part II, Lecture 4 – Vectors in Polar Coordinates Unlimited
    • Part III, Lecture 1 – n-Dimensional Vector Spaces Unlimited
    • Part III, Lecture 2 – Calculus of Several Variables Unlimited
    • Part III, Lecture 3 – Directional Derivatives Unlimited
    • Part III, Lecture 4 – The Chain Rule Unlimited
    • Part III, Lecture 5 – Integrals Involving Parameters Unlimited
    • Part III, Lecture 6 – Exact Differentials Unlimited
    • Part IV, Lecture 1 – Linearity Revisited Unlimited
    • Part IV, Lecture 2 – The “Game” of Matrices Unlimited
    • Part IV, Lecture 3 – Inverting a Matrix Unlimited
    • Part IV, Lecture 4 – Inverting More General Systems of Equations Unlimited
    • Part IV, Lecture 5 – Maxima and Minima in Several Variables Unlimited
    • Part V, Lecture 1 – Double Multiple Sums Unlimited
    • Part V, Lecture 2 – The Fundamental Theorem Unlimited
    • Part V, Lecture 3 – Multiple Integration and the Jacobian Unlimited
    • Part V, Lecture 4 – Introduction to Line Integrals Unlimited
    • Part V, Lecture 5 – Green’s Theorem Unlimited

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