1636 vector calculus

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