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

Chapter 12

Vector-Valued Functions

Copyright © Houghton Mifflin Company. All rights reserved. 12-2

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

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