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Vector Fields

Vector Fields. A brief introduction. A set of outputs (range!). A set of inputs (domain!). A “rule” that takes any input and yields an output. Functions---The Big Picture. Our Function “zoo”.

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Vector Fields

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  1. Vector Fields A brief introduction

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

  3. Our Function “zoo” • We have been concentrating mostly on functions with two or three input (real) variables and one output (real) variable. In Calc A and Calc B we study functions with one real input variable and one real output variable. These are called “Scalar Fields.”

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

  5. Scalar Fields in Higher Dimensions Harder to picture… Examples?

  6. Vector Fields • Functions in which the inputs are real numbers of vectors and the outputs are also vectors are called “vector fields.” • We will still concentrate on vectors with 2 or 3 coordinates to make these things easier to picture. But really we can work in any dimension.

  7. Some special CasesParametrically Defined Curves In the plane In 3-dimensional space

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

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

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

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