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# ch12 - Math 241.1 Definitions and Examples of Vector Valued...

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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 won’t go into detail but it’s 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 won’t. In essence the derivative of a VVF is found by taking the derivatives of the components.

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ch12 - Math 241.1 Definitions and Examples of Vector Valued...

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