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CourseRES.18-00726 lectures13 h 50 min

Calculus Revisited: Multivariable Calculus

Prof. Herbert Gross · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Acknowledgements

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

Lectures

Part I: Vector Arithmetic

  1. Lecture 1: The "Game" of Mathematics 21 min · Video
  2. Lecture 2: "Arrow" Arithmetic 29 min · Video
  3. Lecture 3: Three-Dimensional Vectors 27 min · Video
  4. Lecture 4: The Dot Product 31 min · Video
  5. Lecture 5: The Cross Product 33 min · Video
  6. Lecture 6: Equations of Lines & Planes 29 min · Video

Part II: Vector Calculus

  1. Lecture 1: Vector Functions of a Scalar Variable 39 min · Video
  2. Lecture 2: Tangential & Normal Vectors 29 min · Video
  3. Lecture 3: Polar Coordinates 31 min · Video
  4. Lecture 4: Vectors in Polar Coordinates 29 min · Video

Part III: Partial Derivatives

  1. Lecture 1: n-Dimensional Vector Spaces 34 min · Video
  2. Lecture 2: Calculus of Several Variables 36 min · Video
  3. Lecture 3: Directional Derivatives 34 min · Video
  4. Lecture 4: The Chain Rule 39 min · Video
  5. Lecture 5: Integrals Involving Parameters 28 min · Video
  6. Lecture 6: Exact Differentials 30 min · Video

Part IV: Matrix Algebra

  1. Lecture 1: Linearity Revisited 48 min · Video
  2. Lecture 2: The "Game" of Matrices 42 min · Video
  3. Lecture 3: Inverting a Matrix 46 min · Video
  4. Lecture 4: Inverting More General Systems of Equations 29 min · Video
  5. Lecture 5: Maxima and Minima in Several Variables 35 min · Video

Part V: Multiple Integration

  1. Lecture 1: Double Multiple Sums 30 min · Video
  2. Lecture 2: The Fundamental Theorem 27 min · Video
  3. Lecture 3: Multiple Integration and the Jacobian 34 min · Video
  4. Lecture 4: Introduction to Line Integrals 25 min · Video
  5. Lecture 5: Green's Theorem 29 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Herbert Gross
Term
Fall 2011
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Herbert Gross. Calculus Revisited: Multivariable Calculus. Fall 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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