OCW Scholar: Multivariable Calculus

Consequences of Stokes' Theorem

Play Episode Listen Later Dec 19, 2017 11:12

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

consequences stokes theorem

More Stokes' Theorem

Play Episode Listen Later Dec 19, 2017 8:20

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

stokes theorem

Simply connected regions

Play Episode Listen Later Dec 19, 2017 14:46

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

connected regions

Extended Stokes' Theorem

Play Episode Listen Later Dec 19, 2017 15:40

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

stokes theorem

Stokes' Theorem

Play Episode Listen Later Dec 19, 2017 17:33

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

stokes theorem

Conservative fields and exact differentials

Play Episode Listen Later Dec 19, 2017 14:51

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

conservatives fields exact differentials

Line integral on a helix

Play Episode Listen Later Dec 19, 2017 11:13

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integral helix

Del and the product rule

Play Episode Listen Later Dec 19, 2017 8:29

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

product rule

Extended Gauss' Theorem

Play Episode Listen Later Dec 19, 2017 18:52

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

theorem

Flux and the divergence theorem

Play Episode Listen Later Dec 19, 2017 11:58

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

flux divergence theorem

Flux

Play Episode Listen Later Dec 19, 2017 11:17

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

flux

Flux through surfaces

Play Episode Listen Later Dec 19, 2017 11:21

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

flux surfaces

Flux through a square

Play Episode Listen Later Dec 19, 2017 10:01

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

square flux

Flux through easy surfaces

Play Episode Listen Later Dec 19, 2017 6:47

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

flux surfaces

Gravity and a half-sphere

Play Episode Listen Later Dec 19, 2017 11:13

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

gravity sphere

Average distance on a sphere

Play Episode Listen Later Dec 19, 2017 12:59

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

average distance sphere

Moment of inertia of a cylinder

Play Episode Listen Later Dec 19, 2017 10:00

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

inertia cylinder

Average height

Play Episode Listen Later Dec 19, 2017 14:40

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

average height

Volume in cylindrical coordinates

Play Episode Listen Later Dec 19, 2017 18:06

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

coordinates

Domains of vector fields

Play Episode Listen Later Dec 19, 2017 13:40

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

fields vector domains

Extended Green's Theorem

Play Episode Listen Later Dec 19, 2017 23:18

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

theorem

Green's Theorem in normal form

Play Episode Listen Later Dec 19, 2017 11:03

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

normal theorem

Flux across a curve

Play Episode Listen Later Dec 19, 2017 14:26

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

curve flux

Application of Green's theorem

Play Episode Listen Later Dec 19, 2017 7:14

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

application theorem

Green's Theorem: area under an arch

Play Episode Listen Later Dec 19, 2017 8:36

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

arch theorem

Green's Theorem: an off center circle

Play Episode Listen Later Dec 19, 2017 7:32

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

circle theorem off center

Potentials of gradient fields

Play Episode Listen Later Dec 19, 2017 11:22

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

fields potentials gradient

Non-conservative vector fields

Play Episode Listen Later Dec 19, 2017 10:00

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

conservatives fields vector

Fundamental theorem of line integrals

Play Episode Listen Later Dec 19, 2017 11:08

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integrals fundamental theorem

Line integrals by geometric reasoning

Play Episode Listen Later Dec 19, 2017 10:34

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

reasoning geometric integrals

Line integrals: path dependence

Play Episode Listen Later Dec 19, 2017 15:31

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

dependence integrals

Line integrals: parametrization independence

Play Episode Listen Later Dec 19, 2017 12:31

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

independence integrals

Change of variables

Play Episode Listen Later Dec 19, 2017 19:56

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

variables

Integral of exp(-x^2)

Play Episode Listen Later Dec 19, 2017 9:34

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integral

Change of variables

Play Episode Listen Later Dec 19, 2017 9:17

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

variables

Integrals with density

Play Episode Listen Later Dec 19, 2017 15:36

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

density integrals

Integration in polar coordinates

Play Episode Listen Later Dec 19, 2017 17:33

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integration polar coordinates

Changing the order of integration

Play Episode Listen Later Dec 19, 2017 6:03

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integration

Regions of integration

Play Episode Listen Later Dec 19, 2017 17:46

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

integration regions

Gradients - composition

Play Episode Listen Later Dec 19, 2017 10:21

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

composition gradients

The chain rule with constraints

Play Episode Listen Later Dec 19, 2017 15:15

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

constraints chain rule

Lagrange multipliers (3 variables)

Play Episode Listen Later Dec 19, 2017 13:16

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

variables multipliers lagrange

Lagrange multipliers

Play Episode Listen Later Dec 19, 2017 10:17

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

multipliers lagrange

Gradient and directional derivative

Play Episode Listen Later Dec 19, 2017 13:33

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

gradient directional derivative

Tangent planes

Play Episode Listen Later Dec 19, 2017 9:01

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

planes tangent

Total differentials and the chain rule

Play Episode Listen Later Dec 19, 2017 11:33

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

differentials chain rule

Max/Min

Play Episode Listen Later Dec 19, 2017 13:58

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

Second derivative test

Play Episode Listen Later Dec 19, 2017 8:38

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

derivative

Least squares

Play Episode Listen Later Dec 19, 2017 9:04

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

squares

Tangent plane approximation

Play Episode Listen Later Dec 19, 2017 6:55

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

plane tangent approximation

Partial derivatives

Play Episode Listen Later Dec 19, 2017 5:19

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

partial derivatives

OCW Scholar: Multivariable Calculus

Search for episodes from OCW Scholar: Multivariable Calculus with a specific topic:

Latest episodes from OCW Scholar: Multivariable Calculus

Consequences of Stokes' Theorem

More Stokes' Theorem

Simply connected regions

Extended Stokes' Theorem

Stokes' Theorem

Conservative fields and exact differentials

Line integral on a helix

Del and the product rule

Extended Gauss' Theorem

Flux and the divergence theorem

Flux

Flux through surfaces

Flux through a square

Flux through easy surfaces

Gravity and a half-sphere

Average distance on a sphere

Moment of inertia of a cylinder

Average height

Volume in cylindrical coordinates

Domains of vector fields

Extended Green's Theorem

Green's Theorem in normal form

Flux across a curve

Application of Green's theorem

Green's Theorem: area under an arch

Green's Theorem: an off center circle

Potentials of gradient fields

Non-conservative vector fields

Fundamental theorem of line integrals

Line integrals by geometric reasoning

Line integrals: path dependence

Line integrals: parametrization independence

Change of variables

Integral of exp(-x^2)

Change of variables

Integrals with density

Integration in polar coordinates

Changing the order of integration

Regions of integration

Gradients - composition

The chain rule with constraints

Lagrange multipliers (3 variables)

Lagrange multipliers

Gradient and directional derivative

Tangent planes

Total differentials and the chain rule

Max/Min

Second derivative test

Least squares

Tangent plane approximation

Partial derivatives

Claim OCW Scholar: Multivariable Calculus

On the way!