1. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions a. Vector functions, pp. 762, 764 Vector functions, pp. 762, 764 b. Def. 13.1.1, p. 764 Def. 13.1.1, p. 764 c. Limit Rules, p. 765 Limit Rules, p. 765 d. (13.1.4), p765 (13.1.4), p765 e. Continuity and differentiability, p. 766 Continuity and differentiability, p. 766 f. Integration, p. 767 Integration, p. 767 g. Properties of the integral, pp. 768, 769 Properties of the integral, pp. 768, 769 Differentiation Formulas a. Differentiation rules, p. 772 Differentiation rules, p. 772 b. Differentiation rules, Leibniz’s notation, p. 774 Differentiation rules, Leibniz’s notation, p. 774 c. (13.2.3), (13.2.4), pp. 774, 775 (13.2.3), (13.2.4), pp. 774, 775 Curves a. Differentiable curves, etc., p. 776 Differentiable curves, etc., p. 776 b. Tangent vector, direction of tangent vector, p. 778, figure 13.3.5 Tangent vector, direction of tangent vector, p. 778, figure 13.3.5 c. Tangent line, p. 779 Tangent line, p. 779 d. Unit tangent vector (13.3.3), p. 781 Unit tangent vector (13.3.3), p. 781 e. Principal normal vector (13.3.4), p. 781 Principal normal vector (13.3.4), p. 781 f. Osculating plane, p. 781 Osculating plane, p. 781 Arc Length a. Arc length (13.4.1), p. 787, Figures 13.4.1 – 2 Arc length (13.4.1), p. 787, Figures 13.4.1 – 2 b. Arc length formula, Theorem 13.4.2, p. 788 Arc length formula, Theorem 13.4.2, p. 788 Curvilinear Motion; Curvature a. (13.5.1), (13.5.2), p. 794, Figure 13.5.1 (13.5.1), (13.5.2), p. 794, Figure 13.5.1 b. Curvature, (13.5.3), p. 796, figure 13.5.3 Curvature, (13.5.3), p. 796, figure 13.5.3 c. Curvature of a twice differentiable function, (13.5.4), p. 797 Curvature of a twice differentiable function, (13.5.4), p. 797 d. Curvature, curve given parametrically, (13.5.5), p. 797 Curvature, curve given parametrically, (13.5.5), p. 797 e. Curvature of space curves, (13.5.6), (13.5.7), p. 800, figure 13.5.6 Curvature of space curves, (13.5.6), (13.5.7), p. 800, figure 13.5.6 f. Components of acceleration, (13.5.8), p. 801 Components of acceleration, (13.5.8), p. 801 g. (13.5.9), (13.5.10), (13.5.11), p. 802 (13.5.9), (13.5.10), (13.5.11), p. 802 Chapter 13: Vector Calculus

2. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Vector functions, pp. 762, 764

3. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Def. 13.1.1, p. 764

4. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Limit Rules, p. 765

5. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions (13.1.4), p765

6. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Continuity and differentiability, p. 766

7. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Integration, p. 767

8. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vector Functions Properties of the integral, pp. 768, 769

9. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Differentiation Formulas Differentiation rules, p. 772

10. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Differentiation Formulas Differentiation rules, Leibniz’s notation, p. 774

11. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Differentiation Formulas (13.2.3), (13.2.4), pp. 774, 775

12. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Differentiable curves, etc., p. 776

13. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Tangent vector, direction of tangent vector, p. 778, figure 13.3.5

14. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Tangent line, p. 779

15. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Unit tangent vector (13.3.3), p. 781

16. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Principal normal vector (13.3.4), p. 781

17. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curves Osculating plane, p. 781

18. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Arc Length Arc length (13.4.1), p. 787, Figures 13.4.1-2

19. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Arc Length Arc length formula, Theorem 13.4.2, p. 788

20. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature (13.5.1), (13.5.2), p. 794, Figure 13.5.1

21. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature Curvature, (13.5.3), p. 796, figure 13.5.3

22. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature Curvature of a twice differentiable function, (13.5.4), p. 797

23. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature Curvature, curve given parametrically, (13.5.5), p. 797

24. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature Curvature of space curves, (13.5.6), (13.5.7), p. 800, figure 13.5.6

25. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature Components of acceleration, (13.5.8), p. 801

26. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Curvilinear Motion; Curvature (13.5.9), (13.5.10), (13.5.11), p. 802