Канал: Matthew Russell

241 test 3 review: 40

241 test 3 review: 40

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241 final examination review: 6-7

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241 final examination review: 12-13

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241 test 4 review: 37-38

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241 test 4 review: 50

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241 test 4 review: 32-34

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241 test 2 review: 27-29

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241 test 2 review: 33-35

quadric surfaces overview

quadric surfaces overview

curvature overview

curvature overview

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251 final examination review: #8

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251 final examination review: #1-#2

another Stokes verification

another Stokes verification

vector line integrals: flux

vector line integrals: flux

Stokes's Theorem

Stokes's Theorem

closed surfaces and Stokes's theorem

closed surfaces and Stokes's theorem

a lightbulb

a lightbulb

curl and gradient

curl and gradient

another verification of the divergence theorem

another verification of the divergence theorem

three uses of del

three uses of del

divergence and curl

divergence and curl

divergence

divergence

statement of the divergence theorem

statement of the divergence theorem

applying the divergence theorem

applying the divergence theorem

curl

curl

applying Stokes's theorem

applying Stokes's theorem

scalar surface integrals

scalar surface integrals

flux over upper hemisphere

flux over upper hemisphere

first example of a scalar surface integral

first example of a scalar surface integral

surface integrals introduction and parametrization guide

surface integrals introduction and parametrization guide

scalar surface integral example

scalar surface integral example

divergence theorem verification

divergence theorem verification

Stokes's Theorem verification #1

Stokes's Theorem verification #1

introduction to parametrizations

introduction to parametrizations

surface area formula

surface area formula

parameterization of a sphere

parameterization of a sphere

surface area of implicitly-defined surfaces

surface area of implicitly-defined surfaces

something like a football

something like a football

part of a cone

part of a cone

surface area of a sphere

surface area of a sphere

introduction to parameterized surfaces

introduction to parameterized surfaces

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135/151 test 3 review: #45

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k-component of curl

k-component of curl

flux-divergence Green's theorem

flux-divergence Green's theorem

summary of 16.3

summary of 16.3

circulation-curl Green's theorem

circulation-curl Green's theorem

conservative fields are gradient fields

conservative fields are gradient fields

flow and vector line integrals

flow and vector line integrals

alternate notation for vector line integrals

alternate notation for vector line integrals

work and vector line integrals

work and vector line integrals

introduction to vector line integrals

introduction to vector line integrals

flux across a curve

flux across a curve

divergence

divergence

definitions of path independence, conservative, potential function

definitions of path independence, conservative, potential function

area with Green's theorem

area with Green's theorem

fundamental theorem of line integrals

fundamental theorem of line integrals

Green's theorem and the loop property

Green's theorem and the loop property

the loop property

the loop property

vortex field

vortex field

scalar line integrals introduction

scalar line integrals introduction

scalar line integrals example 2

scalar line integrals example 2

vector fields

vector fields

sketching a vector field

sketching a vector field

additivity for scalar line integrals

additivity for scalar line integrals

component test for conservative vector fields, and finding potential functions

component test for conservative vector fields, and finding potential functions

applying flux-divergence version of Green's theorem

applying flux-divergence version of Green's theorem

applying circulation-curl version of Green's theorem

applying circulation-curl version of Green's theorem

additivity for vector line integrals

additivity for vector line integrals

scalar line integral example

scalar line integral example

path independence motivation

path independence motivation

two fundamental theorems of calculus

two fundamental theorems of calculus

comparing vector and scalar line integrals

comparing vector and scalar line integrals

density with scalar line integrals

density with scalar line integrals

verifying Green's theorem on the unit circle

verifying Green's theorem on the unit circle

a clever application of Green's theorem

a clever application of Green's theorem

using the fundamental theorem of line integrals

using the fundamental theorem of line integrals

vector line integral example 1

vector line integral example 1

maps/transformations/change of variables

maps/transformations/change of variables

simplifying the integrand

simplifying the integrand

determining the transformation

determining the transformation

nonlinear change of variables

nonlinear change of variables

triple integral interpretation

triple integral interpretation

triangle linear map

triangle linear map

an interesting region

an interesting region

trickier spherical integral 1

trickier spherical integral 1

substitution for double integrals

substitution for double integrals

trickier spherical integral 2

trickier spherical integral 2

unknown region integration

unknown region integration

average value for triple integrals

average value for triple integrals

cylindrical coordinates

cylindrical coordinates

polar coordinates integration: example 3

polar coordinates integration: example 3

tetrahedron

tetrahedron

substitution revisited

substitution revisited

intersecting surfaces

intersecting surfaces

ice cream cone

ice cream cone

second polar area example

second polar area example

first substitution example: linear map

first substitution example: linear map

example of integrating with spherical coordinates

example of integrating with spherical coordinates

where the r comes from

where the r comes from

Jacobians

Jacobians

integrating with spherical coordinates

integrating with spherical coordinates

another example of integrating with spherical coordinates

another example of integrating with spherical coordinates

converting with spherical coordinates 2

converting with spherical coordinates 2

converting with spherical coordinates 1

converting with spherical coordinates 1

introduction to spherical coordinates

introduction to spherical coordinates

polar coordinates integration: example 5

polar coordinates integration: example 5

3-variable Jacobian

3-variable Jacobian

cone volume

cone volume