Chapter 13 Vector Calculus Vector Functions a Vector

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Chapter 13: Vector Calculus Vector Functions a. Vector functions, pp. 762, 764 b. Def.

Chapter 13: Vector Calculus Vector Functions a. Vector functions, pp. 762, 764 b. Def. 13. 1. 1, p. 764 c. Limit Rules, p. 765 d. (13. 1. 4), p 765 e. Continuity and differentiability, p. 766 f. Integration, p. 767 g. Properties of the integral, pp. 768, 769 Differentiation Formulas a. Differentiation rules, p. 772 b. Differentiation rules, Leibniz’s notation, p. 774 c. (13. 2. 3), (13. 2. 4), pp. 774, 775 Curves a. Differentiable curves, etc. , p. 776 b. Tangent vector, direction of tangent vector, p. 778, figure 13. 3. 5 c. Tangent line, p. 779 d. Unit tangent vector (13. 3. 3), p. 781 e. Principal normal vector (13. 3. 4), p. 781 f. Osculating plane, p. 781 Arc Length a. Arc length (13. 4. 1), p. 787, Figures 13. 4. 1 – 2 b. 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 b. Curvature, (13. 5. 3), p. 796, figure 13. 5. 3 c. Curvature of a twice differentiable function, (13. 5. 4), p. 797 d. 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 f. Components of acceleration, (13. 5. 8), p. 801 g. (13. 5. 9), (13. 5. 10), (13. 5. 11), p. 802 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 Main Menu Salas, Hille, Etgen Calculus: One

Vector Functions Vector functions, pp. 762, 764 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 Main Menu Salas, Hille, Etgen Calculus:

Vector Functions Def. 13. 1. 1, p. 764 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 Main Menu Salas, Hille, Etgen Calculus: One and

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

Vector Functions (13. 1. 4), p 765 Main Menu Salas, Hille, Etgen Calculus: One

Vector Functions (13. 1. 4), p 765 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 Main Menu Salas, Hille, Etgen Calculus: One

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

Vector Functions Integration, p. 767 Main Menu Salas, Hille, Etgen Calculus: One and Several

Vector Functions Integration, p. 767 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 Main Menu Salas, Hille, Etgen

Vector Functions Properties of the integral, pp. 768, 769 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 Main Menu Salas, Hille, Etgen Calculus: One and

Differentiation Formulas Differentiation rules, p. 772 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 Main Menu Salas, Hille, Etgen Calculus:

Differentiation Formulas Differentiation rules, Leibniz’s notation, p. 774 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 Main Menu Salas,

Differentiation Formulas (13. 2. 3), (13. 2. 4), pp. 774, 775 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 Main Menu Salas, Hille, Etgen Calculus: One

Curves Differentiable curves, etc. , p. 776 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 Main

Curves Tangent vector, direction of tangent vector, p. 778, figure 13. 3. 5 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curves Tangent line, p. 779 Main Menu Salas, Hille, Etgen Calculus: One and Several

Curves Tangent line, p. 779 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 Main Menu Salas, Hille, Etgen

Curves Unit tangent vector (13. 3. 3), p. 781 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 Main Menu Salas, Hille, Etgen

Curves Principal normal vector (13. 3. 4), p. 781 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curves Osculating plane, p. 781 Main Menu Salas, Hille, Etgen Calculus: One and Several

Curves Osculating plane, p. 781 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

Arc Length Arc length (13. 4. 1), p. 787, Figures 13. 4. 1 -2 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 Main Menu Salas,

Arc Length Arc length formula, Theorem 13. 4. 2, p. 788 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.

Curvilinear Motion; Curvature (13. 5. 1), (13. 5. 2), p. 794, Figure 13. 5. 1 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curvilinear Motion; Curvature, (13. 5. 3), p. 796, figure 13. 5. 3 Main Menu

Curvilinear Motion; Curvature, (13. 5. 3), p. 796, figure 13. 5. 3 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curvilinear Motion; Curvature of a twice differentiable function, (13. 5. 4), p. 797 Main

Curvilinear Motion; Curvature of a twice differentiable function, (13. 5. 4), p. 797 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curvilinear Motion; Curvature, curve given parametrically, (13. 5. 5), p. 797 Main Menu Salas,

Curvilinear Motion; Curvature, curve given parametrically, (13. 5. 5), p. 797 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Curvilinear Motion; Curvature of space curves, (13. 5. 6), (13. 5. 7), p. 800,

Curvilinear Motion; Curvature of space curves, (13. 5. 6), (13. 5. 7), p. 800, figure 13. 5. 6 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 Main Menu Salas,

Curvilinear Motion; Curvature Components of acceleration, (13. 5. 8), p. 801 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

Curvilinear Motion; Curvature (13. 5. 9), (13. 5. 10), (13. 5. 11), p. 802 Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

16 VECTOR CALCULUS VECTOR CALCULUS In this chapter16 VECTOR CALCULUS VECTOR CALCULUS In this chapter
17 VECTOR CALCULUS VECTOR CALCULUS In this chapter17 VECTOR CALCULUS VECTOR CALCULUS In this chapter
16 VECTOR CALCULUS VECTOR CALCULUS Here we define16 VECTOR CALCULUS VECTOR CALCULUS Here we define
16 VECTOR CALCULUS VECTOR CALCULUS 16 8 Stokes16 VECTOR CALCULUS VECTOR CALCULUS 16 8 Stokes
16 VECTOR CALCULUS VECTOR CALCULUS 16 9 The16 VECTOR CALCULUS VECTOR CALCULUS 16 9 The
16 VECTOR CALCULUS VECTOR CALCULUS 16 4 Greens16 VECTOR CALCULUS VECTOR CALCULUS 16 4 Greens
16 VECTOR CALCULUS VECTOR CALCULUS 16 3 Fundamental16 VECTOR CALCULUS VECTOR CALCULUS 16 3 Fundamental
16 VECTOR CALCULUS VECTOR CALCULUS So far we16 VECTOR CALCULUS VECTOR CALCULUS So far we
17 VECTOR CALCULUS VECTOR CALCULUS 17 3 Fundamental17 VECTOR CALCULUS VECTOR CALCULUS 17 3 Fundamental
17 VECTOR CALCULUS VECTOR CALCULUS 17 9 The17 VECTOR CALCULUS VECTOR CALCULUS 17 9 The
17 VECTOR CALCULUS VECTOR CALCULUS So far we17 VECTOR CALCULUS VECTOR CALCULUS So far we
17 VECTOR CALCULUS VECTOR CALCULUS 17 2 Line17 VECTOR CALCULUS VECTOR CALCULUS 17 2 Line
17 VECTOR CALCULUS VECTOR CALCULUS 17 9 The17 VECTOR CALCULUS VECTOR CALCULUS 17 9 The
17 VECTOR CALCULUS VECTOR CALCULUS 17 7 Surface17 VECTOR CALCULUS VECTOR CALCULUS 17 7 Surface
16 VECTOR CALCULUS VECTOR CALCULUS 16 7 Surface16 VECTOR CALCULUS VECTOR CALCULUS 16 7 Surface
17 VECTOR CALCULUS VECTOR CALCULUS Here we define17 VECTOR CALCULUS VECTOR CALCULUS Here we define
17 VECTOR CALCULUS VECTOR CALCULUS 17 8 Stokes17 VECTOR CALCULUS VECTOR CALCULUS 17 8 Stokes
CHAPTER FOUR CALCULUS CALCULUS ponential CALCULUS thmic ariCHAPTER FOUR CALCULUS CALCULUS ponential CALCULUS thmic ari
14 VECTOR FUNCTIONS VECTOR FUNCTIONS The functions that14 VECTOR FUNCTIONS VECTOR FUNCTIONS The functions that
13 VECTOR FUNCTIONS VECTOR FUNCTIONS The functions that13 VECTOR FUNCTIONS VECTOR FUNCTIONS The functions that
Vector Calculus Examples of Vector Quantities Vector isVector Calculus Examples of Vector Quantities Vector is
16 Vector Calculus 16 1 Vector Fields Vector16 Vector Calculus 16 1 Vector Fields Vector
Calculus Differentiation Calculus Differentiation dydx y Calculus DifferentiationCalculus Differentiation Calculus Differentiation dydx y Calculus Differentiation
Vector and Vector Resolution Scalar Vector Vectors VectorVector and Vector Resolution Scalar Vector Vectors Vector