calc 4 - midterm 1 theorems

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4 Terms

1
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Green’s Theorem

counterclockwise - negative

clockwise - positive

  • C is positively oriented, piecewise smooth, simple closed curve

  • D is the region bounded by C

  • F must have continuous partial derivatives on an open region containing D

<p>counterclockwise - negative</p><p>clockwise - positive</p><ul><li><p>C is positively oriented, piecewise smooth, simple closed <strong>curve</strong></p></li><li><p>D is the region bounded by C</p></li><li><p>F must have continuous partial derivatives on an open region <em>containing </em>D</p></li></ul><p></p>
2
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Stoke’s Theorem

  • S is oriented, piecewise smooth surface bounded by C

  • C is positively oriented

  • F has continuous partial derivatives on and around S

    (S is the surface, D is the domain that defines S)

<ul><li><p>S is oriented, piecewise smooth surface bounded by C</p></li><li><p>C is positively oriented</p></li><li><p>F has continuous partial derivatives on and around S</p><p><em>(S is the surface, D is the domain that defines S)</em></p></li></ul><p></p>
3
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Divergence Theorem

“flux”

  • E is a simple solid region

  • S is the closed surface that bounds E, oriented outwards (pos)

  • F has continuous partial derivatives on an open region containing E

<p>“flux”</p><ul><li><p>E is a simple solid region</p></li><li><p>S is the closed surface that bounds E, oriented outwards (pos)</p></li><li><p>F has continuous partial derivatives on an open region containing E</p></li></ul><p></p>
4
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