The “Zoo” of Vector Analysis

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Presentation transcript:

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

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

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.)

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

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

Trajectories in Space

Trajectories in Space

Trajectories in Space

Trajectories in 3-dimensional space An Example 4 world records: Tallest, Longest, Fastest and Greatest Drop. Steel Dragon Nagashima Spaland, Japan

Scalar Fields A scalar field is one whose output values are real numbers

Scalar Fields in Higher Dimensions Examples?

Vector Fields A vector field is one whose output values are vectors. Examples?

Vector Fields A vector field is one whose output values are vectors. Direction field---if we care only about direction and not magnitude