1. The “Zoo” of Vector Analysis
What are we Studying?
The “Zoo” of Vector Analysis

2. Functions---The Big Picture
A set of inputs
(domain!)
A set of outputs
(range!)
A “rule” that takes any input and yields an output

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. Parametrically Defined Curves
Some Special Cases
Parametrically Defined Curves
In the plane
In 3-dimensional space

5. Parametric Curves in the Plane An Example
Hypotrochoids
(Spirograph, anyone?)

6. Trajectories in Space

7. Trajectories in Space

8. Trajectories in Space

9. Trajectories in 3-dimensional space An 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

11. 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