Title: What are we Studying?
1What are we Studying?
- The Zoo of Vector Analysis
2Functions---The Big Picture
3Our 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.)
4Some Special Cases
Parametrically Defined Curves
In the plane
In 3-dimensional space
5Parametric Curves in the PlaneAn Example
Hypotrochoids
(Spirograph, anyone?)
6Trajectories in Space
7Trajectories in Space
8Trajectories in Space
9Trajectories in 3-dimensional spaceAn Example
4 world records Tallest, Longest, Fastest and
Greatest Drop.
Steel Dragon Nagashima Spaland, Japan
10Scalar Fields
A scalar field is one whose output values are
real numbers
11Scalar Fields in Higher Dimensions
Examples?
12Vector Fields
A vector field is one whose output values are
vectors.
Examples?
13Vector Fields
A vector field is one whose output values are
vectors.
Direction field---if we care only about direction
and not magnitude