# Calculus Revisited: Multivariable Calculus

## by Herbert Gross

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#### Description

This course is a study of the calculus of functions of several variables (vector arithmetic and vector calculus). License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms

Name | Description | Released | Price | ||
---|---|---|---|---|---|

1 | VideoPart I: Vector Arithmetic, Lecture 1: The "Game" of Mathematics | Herb Gross introduces Calculus Revisited part 2 - functions of several variables and discusses the over-arching theme "The Game of Mathematics" | 12/20/11 | Free | View In iTunes |

2 | VideoPart I: Vector Arithmetic, Lecture 2: "Arrow" Arithmetic | Herb Gross reviews the definition of vectors and vector arithmetic. | 5/17/12 | Free | View In iTunes |

3 | VideoPart I: Vector Arithmetic, Lecture 3: Three-Dimensional Vectors | Herb Gross introduces 3-dimensional vectors. | 5/17/12 | Free | View In iTunes |

4 | VideoPart I: Vector Arithmetic, Lecture 4: The Dot Product | Herb Gross motivates the definition of the dot product and shows how to calculate the dot product of two vectors in 3-space. | 12/20/11 | Free | View In iTunes |

5 | VideoPart I: Vector Arithmetic, Lecture 5: The Cross Product | Herb Gross defines the cross product of two vectors. | 12/20/11 | Free | View In iTunes |

6 | VideoPart I: Vector Arithmetic, Lecture 6: Equations of Lines and Planes | Herb Gross discusses the topic of lines and planes in 3-dimensional space. | 12/20/11 | Free | View In iTunes |

7 | VideoPart II: Vector Calculus, Lecture 1: Vector Functions of a Scalar Variable | Herb Gross introduces the topic of Vector Functions of Scalar Variables. | 12/20/11 | Free | View In iTunes |

8 | VideoPart II: Vector Calculus, Lecture 2: Tangential and Normal Vectors | Herb Gross discuss tangential and normal vectors to a point on a function in 2-space analagous to x-y coordinates. | 12/20/11 | Free | View In iTunes |

9 | VideoPart II: Vector Calculus, Lecture 3: Polar Coordinates | Herb Gross defines and demonstrates the use polar coordinates. | 12/20/11 | Free | View In iTunes |

10 | VideoPart II: Vector Calculus, Lecture 4: Vectors in Polar Coordinates | Herb Gross describes Vectors and Polar Coordinates. | 12/20/11 | Free | View In iTunes |

11 | VideoPart III: Partial Derivatives, Lecture 1: n-Dimensional Vector Spaces | Herb Gross describes n-Dimensional Vector Spaces relating definitions to the concept of a mathematical structure. | 12/20/11 | Free | View In iTunes |

12 | VideoPart III: Partial Derivatives, Lecture 2: Calculus of Several Variables | Herb Gross introduces us to the traditional Calculus of Several Variables | 12/20/11 | Free | View In iTunes |

13 | VideoPart III: Partial Derivatives, Lecture 3: Directional Derivatives | Herb Gross defines the Directional Derivative and demonstrates how to calculate it. Herb also emphasizes the importance of this topic in the study of Calculus of Several Variables | 12/20/11 | Free | View In iTunes |

14 | VideoPart III: Partial Derivatives, Lecture 4: The Chain Rule | Herb Gross shows examples of the Chain Rule for several variables. | 12/20/11 | Free | View In iTunes |

15 | VideoPart III: Partial Derivatives, Lecture 5: Integrals Involving Parameters | Herb Gross show how the Chain Rule is involved in finding some integrals involving parameters. | 12/20/11 | Free | View In iTunes |

16 | VideoPart III: Partial Derivatives, Lecture 6: Exact Differentials | Herb Gross discusses Exact Differentials. | 12/20/11 | Free | View In iTunes |

17 | VideoPart IV: Matrix Algebra, Lecture 1: Linearity Revisited | Herb Gross considers linearity in spaces of greater than 2 variables including a discussion of local linearity. | 12/20/11 | Free | View In iTunes |

18 | VideoPart IV: Matrix Algebra, Lecture 2: The "Game" of Matrices | Herb Gross describes the mathematical structure of matrix algebra. | 12/20/11 | Free | View In iTunes |

19 | VideoPart IV: Matrix Algebra, Lecture 3: Inverting a Matrix | Herb Gross illustrates how to invert a square matrix and its relevance to Calculus of several variables. | 12/20/11 | Free | View In iTunes |

20 | VideoPart IV: Matrix Algebra, Lecture 4: Inverting More General Systems of Equations | Herb Gross demonstrates how to invert systems of non-linear equations. | 12/20/11 | Free | View In iTunes |

21 | VideoPart IV: Matrix Algebra, Lecture 5: Maxima and Minima in Several Variables | With our knowledge of Matrix Algebra to help, Herb Gross teaches how to find maxima and minima of functions of several real variables. | 12/20/11 | Free | View In iTunes |

22 | VideoPart V: Multiple Integration, 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. | 12/20/11 | Free | View In iTunes |

23 | VideoPart V: Multiple Integration, Lecture 2: The Fundamental Theorem | Herb Gross illustrates the equivalence of the fundamental theorem of the calculus of one variable to the fundamental theorem of the calculus of several variables. | 12/20/11 | Free | View In iTunes |

24 | VideoPart V: Multiple Integration, Lecture 3: Multiple Integration and the Jacobian | Herb Gross illustrates how the Jacobian arises when changing coordinates in order to calculate a double integral. | 12/20/11 | Free | View In iTunes |

25 | VideoPart V: Multiple Integration, Lecture 4: Introduction to Line Integrals | There is more than one type of integral in calculus of more than one variable. In this lesson, Herb Gross discusses line integrals. | 12/20/11 | Free | View In iTunes |

26 | VideoPart V: Multiple Integration, Lecture 5: Green's Theorem | Herb Gross discusses Green's Theorem: the relationship between line integrals and double integrals over a region in 2-space. | 12/20/11 | Free | View In iTunes |

26 Items |

#### Customer Reviews

##### Listen

Do not even read the comment that says this is a bad course. This is the best!

##### Good Stuff!

Admittedly, Mr. Gross has a different lecture style, which is why I like his material. He often takes a back-door approach to the subject and explains things in a way I never see from contemporary professors. He reveals ideas I had never heard or considered before, so I feel I'm getting a well rounded view of the subject from all angles.

It takes a little patience to get in tune with his thinking, but it's worth the effort. He is pretty funny at times, and often jokes about the seemingly inaccessible nature of some of the concepts.

##### Logical and Clear

Professor Gross goes from one concept to another very clearly and methodically. In his explanations, he has a way of simplifying and connecting concepts that makes one feel at ease with the lessons.

It is remarkable that even without the fanfare and special effects of today's technologies, his videos are able to communicate well to a modern audience the challenging topics of his lectures.

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