1. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals a. Definition 17.1.3, p. 1021 Definition 17.1.3, p. 1021 b. Theorem 17.1.4, p. 1022 Theorem 17.1.4, p. 1022 c. (17.1.5), p. 1023, figure 17.1.2 (17.1.5), p. 1023, figure 17.1.2 d. (17.1.8), p. 1025 (17.1.8), p. 1025 Fundamental Theorem for Line Integrals a. Theorem 17.2.1, p. 1028 Theorem 17.2.1, p. 1028 b. (17.2.2), p. 1028 (17.2.2), p. 1028 Work-Energy Formula; Conservation of Mechanical Energy a. Work-energy formula, (17.3.1), p. 1032 Work-energy formula, (17.3.1), p. 1032 b. Conservative field, potential energy functions, p. 1033 Conservative field, potential energy functions, p. 1033 c. Conservation of mechanical energy, p. 1033 Conservation of mechanical energy, p. 1033 Another Notation for Line Integrals … a. Another notation for line integrals, p. 1036 Another notation for line integrals, p. 1036 b. Line integral with respect to arc length, (17.4.1), p. 1037 Line integral with respect to arc length, (17.4.1), p. 1037 Green’s Theorem a. Green’s theorem, Theorem 17.5.1, p. 1041, figure 17.5.1 Green’s theorem, Theorem 17.5.1, p. 1041, figure 17.5.1 b. Area of a Jordan region, p. 1045 Area of a Jordan region, p. 1045 c. Green’s theorem for annular regions, p. 1047, figure 17.5.10-11 Green’s theorem for annular regions, p. 1047, figure 17.5.10-11 Parametrized Surfaces; Surface Area a. Fundamental vector product, pp. 1054, 1055 Fundamental vector product, pp. 1054, 1055 b. (17.6.1), p. 1055 (17.6.1), p. 1055 c. (17.6.3), p. 1057 (17.6.3), p. 1057 d. Area of surface z=f (x,y), (17.6.4), p. 1060 Area of surface z=f (x,y), (17.6.4), p. 1060 Surface Integrals a. (17.7.2), p. 1064 (17.7.2), p. 1064 b. (17.7.3), p. 1064 (17.7.3), p. 1064 c. Flux of v across S, (17.7.8), p. 1069 Flux of v across S, (17.7.8), p. 1069 Chapter 17: Line Integrals and Surface Integrals The Vector Differential Operator  a. (17.8.1), p. 1074 (17.8.1), p. 1074 b. Gradient of f, p. 1074 Gradient of f, p. 1074 c. (17.8.2), divergence of v, p. 1074 (17.8.2), divergence of v, p. 1074 d. (17.8.3), curl of v, p. 1074 (17.8.3), curl of v, p. 1074 e. Theorems 17.8.4, 17.8.5, pp. 1076, 1077 Theorems 17.8.4, 17.8.5, pp. 1076, 1077 f. The Laplacian, p. 1077 The Laplacian, p. 1077 The Divergence Theorem a. Theorem 17.9.2, p. 1080 Theorem 17.9.2, p. 1080 Stokes’s Theorem a. Theorem 17.10.1, Stokes’s theorem, p. 1087 Theorem 17.10.1, Stokes’s theorem, p. 1087 b. (17.10.2), p. 1089 (17.10.2), p. 1089

2. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals Definition 17.1.3, p. 1021

3. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals Theorem 17.1.4, p. 1022

4. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals (17.1.5), p. 1023, figure 17.1.2

5. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals (17.1.8), p. 1025

6. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Fundamental Theorem for Line Integrals Theorem 17.2.1, p. 1028

7. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Fundamental Theorem for Line Integrals (17.2.2), p. 1028

8. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Work-Energy Formula; Conservation of Mechanical Energy Work-energy formula, (17.3.1), p. 1032

9. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Work-Energy Formula; Conservation of Mechanical Energy Conservative field, potential energy functions, p. 1033

10. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Work-Energy Formula; Conservation of Mechanical Energy Conservation of mechanical energy, p. 1033

11. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Another Notation for Line Integrals… Another notation for line integrals, p. 1036

12. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Another Notation for Line Integrals… Line integral with respect to arc length, (17.4.1), p. 1037

13. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Green’s Theorem Green’s theorem, Theorem 17.5.1. p. 1041, figure 17.5.1

14. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Green’s Theorem Area of a Jordan region, p. 1045

15. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Green’s Theorem Green’s theorem for annular regions, p. 1047, figure 17.5.10-11

16. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Parametrized Surfaces; Surface Area Fundamental vector product, pp. 1054, 1055

17. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Parametrized Surfaces; Surface Area (17.6.1), p. 1055

18. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Parametrized Surfaces; Surface Area (17.6.3), p. 1057

19. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Parametrized Surfaces; Surface Area Area of surface z=f (x,y), (17.6.4), p. 1060

20. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Surface Integrals (17.7.2), p. 1064

21. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Surface Integrals (17.7.3), p. 1064

22. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Surface Integrals Flux of v across S, (17.7.8), p. 1069

23. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  (17.8.1), p. 1074

24. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  Gradient of f, p. 1074

25. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  (17.8.2), divergence of v, p. 1074

26. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  (17.8.3), curl of v, p. 1074

27. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  Theorems 17.8.4, 17.8.5, pp. 1076, 1077

28. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Vector Differential Operator  The Laplacian, p. 1077

29. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Divergence Theorem Theorem 17.9.2, p. 1080

30. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Stokes’s Theorem Theorem 17.10.1, Stokes’s theorem, p. 1087

31. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Stokes’s Theorem (17.10.2), p. 1089