Transcript Chapter 1: Precalculus Review Topics

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