Math 241 Chapter 12
Dr. Justin O. WyssGallifent
§
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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 Spring '08
 staff
 Math, Derivative, Vector Space, Defn, VVF

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