Calculus Revisited: Multivariable Calculus

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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

Herbert Gross

May 17, 2012 LATEST EPISODE
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31m AVG DURATION
26 EPISODES

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Latest episodes from Calculus Revisited: Multivariable Calculus

Part I: Vector Arithmetic, Lecture 3: Three-Dimensional Vectors

Play Episode Listen Later May 17, 2012 26:42

Herb Gross introduces 3-dimensional vectors.

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Part I: Vector Arithmetic, Lecture 2: "Arrow" Arithmetic

Play Episode Listen Later May 17, 2012 28:01

Herb Gross reviews the definition of vectors and vector arithmetic.

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Part V: Multiple Integration, Lecture 5: Green's Theorem

Play Episode Listen Later Dec 20, 2011 28:40

Herb Gross discusses Green's Theorem: the relationship between line integrals and double integrals over a region in 2-space.

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Part V: Multiple Integration, Lecture 2: The Fundamental Theorem

Play Episode Listen Later Dec 20, 2011 26:33

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.

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Part V: Multiple Integration, Lecture 3: Multiple Integration and the Jacobian

Play Episode Listen Later Dec 20, 2011 33:06

Herb Gross illustrates how the Jacobian arises when changing coordinates in order to calculate a double integral.

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Part V: Multiple Integration, Lecture 4: Introduction to Line Integrals

Play Episode Listen Later Dec 20, 2011 24:07

There is more than one type of integral in calculus of more than one variable. In this lesson, Herb Gross discusses line integrals.

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Part V: Multiple Integration, Lecture 1: Double Multiple Sums

Play Episode Listen Later Dec 20, 2011 29:58

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.

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Part IV: Matrix Algebra, Lecture 3: Inverting a Matrix

Play Episode Listen Later Dec 20, 2011 45:42

Herb Gross illustrates how to invert a square matrix and its relevance to Calculus of several variables.

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Part IV: Matrix Algebra, Lecture 5: Maxima and Minima in Several Variables

Play Episode Listen Later Dec 20, 2011 34:48

With our knowledge of Matrix Algebra to help, Herb Gross teaches how to find maxima and minima of functions of several real variables.

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Part IV: Matrix Algebra, Lecture 2: The "Game" of Matrices

Play Episode Listen Later Dec 20, 2011 41:12

Herb Gross describes the mathematical structure of matrix algebra.

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Part IV: Matrix Algebra, Lecture 1: Linearity Revisited

Play Episode Listen Later Dec 20, 2011 47:54

Herb Gross considers linearity in spaces of greater than 2 variables including a discussion of local linearity.

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Part IV: Matrix Algebra, Lecture 4: Inverting More General Systems of Equations

Play Episode Listen Later Dec 20, 2011 28:38

Herb Gross demonstrates how to invert systems of non-linear equations.

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Part III: Partial Derivatives, Lecture 3: Directional Derivatives

Play Episode Listen Later Dec 20, 2011 33:15

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

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Part III: Partial Derivatives, Lecture 6: Exact Differentials

Play Episode Listen Later Dec 20, 2011 29:23

Herb Gross discusses Exact Differentials.

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Part III: Partial Derivatives, Lecture 4: The Chain Rule

Play Episode Listen Later Dec 20, 2011 38:33

Herb Gross shows examples of the Chain Rule for several variables.

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Part III: Partial Derivatives, Lecture 5: Integrals Involving Parameters

Play Episode Listen Later Dec 20, 2011 27:19

Herb Gross show how the Chain Rule is involved in finding some integrals involving parameters.

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Part III: Partial Derivatives, Lecture 2: Calculus of Several Variables

Play Episode Listen Later Dec 20, 2011 35:32

Herb Gross introduces us to the traditional Calculus of Several Variables

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Part II: Vector Calculus, Lecture 3: Polar Coordinates

Play Episode Listen Later Dec 20, 2011 30:59

Herb Gross defines and demonstrates the use polar coordinates.

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Part III: Partial Derivatives, Lecture 1: n-Dimensional Vector Spaces

Play Episode Listen Later Dec 20, 2011 33:04

Herb Gross describes n-Dimensional Vector Spaces relating definitions to the concept of a mathematical structure.

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Part II: Vector Calculus, Lecture 2: Tangential and Normal Vectors

Play Episode Listen Later Dec 20, 2011 28:23

Herb Gross discuss tangential and normal vectors to a point on a function in 2-space analagous to x-y coordinates.

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Part II: Vector Calculus, Lecture 4: Vectors in Polar Coordinates

Play Episode Listen Later Dec 20, 2011 28:04

Herb Gross describes Vectors and Polar Coordinates.

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Part II: Vector Calculus, Lecture 1: Vector Functions of a Scalar Variable

Play Episode Listen Later Dec 20, 2011 38:49

Herb Gross introduces the topic of Vector Functions of Scalar Variables.

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Part I: Vector Arithmetic, Lecture 5: The Cross Product

Play Episode Listen Later Dec 20, 2011 32:13

Herb Gross defines the cross product of two vectors.

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Part I: Vector Arithmetic, Lecture 4: The Dot Product

Play Episode Listen Later Dec 20, 2011 30:05

Herb Gross motivates the definition of the dot product and shows how to calculate the dot product of two vectors in 3-space.

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Part I: Vector Arithmetic, Lecture 6: Equations of Lines and Planes