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What are we Studying?

What are we Studying?. The “Zoo” of Vector Analysis. 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 “zoo”. Calculus C---concentrates (with some exceptions) on Vector Analysis studies

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What are we Studying?

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

  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 “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 CasesParametrically Defined Curves In the plane In 3-dimensional space

  5. Trajectories in Space

  6. Trajectories in Space

  7. Trajectories in Space

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

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

  10. Scalar Fields in Higher Dimensions Examples?

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

  12. 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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