What are we Studying?

1
What are we Studying?

• The Zoo of Vector Analysis

2
Functions---The Big Picture
3
Our zoo

• Calculus C---concentrates (with some exceptions)
  on
• Vector Analysis studies
• (Though our pictures and many applications are
  still in the plane or in 3-space.)

4
Some Special Cases
Parametrically Defined Curves
In the plane
In 3-dimensional space
5
Parametric Curves in the PlaneAn Example
Hypotrochoids
(Spirograph, anyone?)
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Trajectories in Space
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Trajectories in Space
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Trajectories in Space
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Trajectories in 3-dimensional spaceAn Example
4 world records Tallest, Longest, Fastest and
Greatest Drop.
Steel Dragon Nagashima Spaland, Japan
10
Scalar Fields
A scalar field is one whose output values are
real numbers
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Scalar Fields in Higher Dimensions
Examples?
12
Vector Fields
A vector field is one whose output values are
vectors.
Examples?
13
Vector Fields
A vector field is one whose output values are
vectors.
Direction field---if we care only about direction
and not magnitude