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

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Presentation transcript:

Chapter 12 Vector-Valued Functions

Copyright © Houghton Mifflin Company. All rights reserved.12-2 Definition of Vector-Valued Function

Copyright © Houghton Mifflin Company. All rights reserved.12-3 Figure 12.1

Copyright © Houghton Mifflin Company. All rights reserved.12-4 Definition of the Limit of a Vector-Valued Function

Copyright © Houghton Mifflin Company. All rights reserved.12-5 Figure 12.6

Copyright © Houghton Mifflin Company. All rights reserved.12-6 Definition of Continuity of a Vector-Valued Function

Copyright © Houghton Mifflin Company. All rights reserved.12-7 Definition of the Derivative of a Vector-Valued Function

Copyright © Houghton Mifflin Company. All rights reserved.12-8 Figure 12.8

Copyright © Houghton Mifflin Company. All rights reserved.12-9 Theorem 12.1 Differentiation of Vector-Valued Functions

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.2 Properties of the Derivative

Copyright © Houghton Mifflin Company. All rights reserved Definition of Integration of Vector-Valued Functions

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.10

Copyright © Houghton Mifflin Company. All rights reserved Definitions of Velocity and Acceleration

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.16

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.3 Position Function for a Projectile

Copyright © Houghton Mifflin Company. All rights reserved Definition of Unit Tangent Vector

Copyright © Houghton Mifflin Company. All rights reserved Definition of Principal Unit Normal Vector

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.22

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.4 Acceleration Vector

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.5 Tangential and Normal Components of Acceleration

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.24

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.6 Arc Length of a Space Curve

Copyright © Houghton Mifflin Company. All rights reserved Definition of Arc Length Function and Figure 12.29

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.7 Arc Length Parameter

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.31

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.32

Copyright © Houghton Mifflin Company. All rights reserved Definition of Curvature

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.8 Formulas for Curvature

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.34

Copyright © Houghton Mifflin Company. All rights reserved Theorem 12.9 Curvature in Rectangular Coordinates

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.35

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.37

Copyright © Houghton Mifflin Company. All rights reserved Theorem Acceleration, Speed, and Curvature

Copyright © Houghton Mifflin Company. All rights reserved Figure 12.38

Copyright © Houghton Mifflin Company. All rights reserved Summary of Velocity, Acceleration, and Curvature