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Unformatted text preview: Math 241 Chapter 12 Dr. Justin O. Wyss-Gallifent 12.1 Definitions and Examples of Vector Valued Functions 1. Definition: For each t , F ( t ) (or usually, and later, r ( t )) points from the origin to a point on the curve. 2. Classic examples: Circles, helices, lines and line segments, functions. 3. Properties: Without going too far into detail note that VVFs are vectors and so we can do vectorish things with them like F G and f F where f is a regular function. 12.2 Limits and Continuity of VVFs 1. We can define limit the limit of a VVF by taking the limits of the components. We can then define a VVF to be continuous iff the components are continuous. We wont go into detail but its good to be aware that limits exist so that derivatives do. 12.3 Derivatives and Integrals of VVFs 1. We can do this formally with limits but we wont. In essence the derivative of a VVF is found by taking the derivatives of the components....
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08