Chapter 12 Vector-Valued Functions. Copyright © Houghton Mifflin Company. All rights reserved.12-2...

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Chapter 12

Vector-Valued Functions

Definition of Vector-Valued Function

Figure 12.1

Definition of the Limit of a Vector-Valued Function

Figure 12.6

Definition of Continuity of a Vector-Valued Function

Definition of the Derivative of a Vector-Valued Function

Figure 12.8

Theorem 12.1 Differentiation of Vector-Valued Functions

Theorem 12.2 Properties of the Derivative

Definition of Integration of Vector-Valued Functions

Figure 12.10

Definitions of Velocity and Acceleration

Figure 12.16

Theorem 12.3 Position Function for a Projectile

Definition of Unit Tangent Vector

Definition of Principal Unit Normal Vector

Figure 12.22

Theorem 12.4 Acceleration Vector

Theorem 12.5 Tangential and Normal Components of Acceleration

Figure 12.24

Theorem 12.6 Arc Length of a Space Curve

Definition of Arc Length Function and Figure 12.29

Theorem 12.7 Arc Length Parameter

Figure 12.31

Figure 12.32

Definition of Curvature

Theorem 12.8 Formulas for Curvature

Figure 12.34

Theorem 12.9 Curvature in Rectangular Coordinates

Figure 12.35

Figure 12.37

Theorem 12.10 Acceleration, Speed, and Curvature

Figure 12.38

Summary of Velocity, Acceleration, and Curvature

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