1636 vector calculus
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Transcript of 1636 vector calculus
Calculus 5eEarly Transcendentals MultivariableJames Stewart
Chapter 16Vector Calculus
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 2
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
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 3
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
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 4
Section 16.1 Figures 10-12
Examples of computer-generated vector fields
kjiF xzyzyx ),,( kjiF xyzyx 2),,(
kjiF4
),,( zzx
zyzyx
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 5
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
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 6
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.
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 7
A
Section 16.3 Figure 9
The vector field in Example 3
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 8
A
Section 16.6 Figure 5
Grid curves for
Animate u constant
Animate v constant
A
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 9
A
Section 16.6 Figure 10
Computer-generated plot of the graph in Example 8
sinsincossin xzxyxx
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 10
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
© 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 11
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