1. Calculus 5e Early Transcendentals Multivariable James Stewart Chapter 16 Vector Calculus

2. © 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 16.6.5 Figure 16.6.10

3. © 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

4. © 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

5. © 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 11. 12. 13. 14. III IV

6. © 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 15. 16. 17. 18.

7. © 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

8. © 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

9. © 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

10. © 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 III III IVVVI

11. © 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 Theorem for Line Integrals Green’s Theorem Stokes’ Theorem Divergence Theorem    