Week8 Item Download 2023-01-26 00-28-18

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lecture 17 surface integrals relevant section of amath 231 course notes section 3 1 1 2 surfaces are 2 dimensional subsets of r we wish to perform two fundamental integration ...

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...Lecture surface integrals relevant section of amath course notes surfaces are dimensional subsets r we wish to perform two fundamental integration procedures over such scalar functions f x y z s fds examples if then rs ds is the area charge density per unit dq amount in element total q mass dm m fact illustrate can easily compute a sphere sr radius from our knowledge spherical polar coordinates ll simply keep xed remain on volume integral becomes rsin d rz sin derive this result more mathematically later vector at each n where outward normal nds ux through inwhatfollows weshalldevelopamethodtoperformintegrationsoversurfacesbyusingparametriza tions much as did for integrations curves but mention that it may be possible avoid detailed work problem has some nice symmetries special cases occur physics gravity and e g spherically symmetric uids uxes rather straight forward way using denition via parametrization general parametrize express above these parameters shall need say u v dene becau...

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Posted on: 26 Jan 2023 | 4 years ago
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