1636 vector calculus
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Calculus 5eEarly Transcendentals MultivariableJames Stewart
Chapter 16Vector Calculus
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Follow the link to the slide. Then click on the figure to play the animation.
Animations
A
Figure 16.3.9
Figure 16.6.5Figure 16.6.10
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Section 16.1 Figure 1
Air velocity vectors indicating wind speed and direction
(a) 12:00 P.M., June 11, 2002 (b) 4:00 P.M., June 30, 2002
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Section 16.1 Figures 10-12
Examples of computer-generated vector fields
kjiF xzyzyx ),,( kjiF xyzyx 2),,(
kjiF4
),,( zzx
zyzyx
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Section 16.1 Exercises 11-14
I II
xyyx ,),( F
ysyx in ,1),( F
1 ,2),( xxyxF
xyyx /1 ,),( F
11.
12.
13.
14.
III IV
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Section 16.1 Exercises 15-18
I II
III IV
kjiF 32) ,,( zyx
kjiF zzyx 2) ,,(
kjiF 3) ,,( yxzyx
kjiF zyxzyx ),,(
15.
16.
17.
18.
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A
Section 16.3 Figure 9
The vector field in Example 3
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A
Section 16.6 Figure 5
Grid curves for
Animate u constant
Animate v constant
A
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A
Section 16.6 Figure 10
Computer-generated plot of the graph in Example 8
sinsincossin xzxyxx
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Section 16.6 Exercises 11-16
I II III
IV V VI
kjir11. uvvvu sincos),( kjir12. uvuvuvu sincos),(
kjir13. vvuvuvu sincos),( vuzvuyux cos ,sin ,3 14.
,cossin vuux 15. ,4coscos31 uvux 16. uzvuy ,sincos1uz
,4sincos31 uvuy vuuz sin13
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Section 16.10 Summary Box
Summary: Higher-dimensional versions of the Fundamental Theorem
Fundamental Theorem of Calculus
Fundamental Theoremfor Line Integrals
Green’s Theorem
Stokes’ Theorem
Divergence Theorem
)()()( aFbFdxxFb
a
dyQdxPdAyP
xQ
CD
))(())(( afbfdfC
rrr
SFF ddVSE div
rFSF ddC
S curl