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Calc III Ch15 Notes_Part26

# Calc III Ch15 Notes_Part26 - Understanding Recall that the...

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Unformatted text preview: Understanding. . . . Recall that the ﬂux surface integral calculates the volume of ﬂuid that ﬂowing over the surface S per unit time. We talked about a very small “patch” of surface and summing all the volumes of ﬂuid. The triple integral in the divergence theorem is instead looking at a small “cube” and the volume of ﬂuid in/out of the cube. But what about all the cubes that have boundaries with other cubes (imagine a cube whose all 6 sides are shared with others), what happens here? Thus, the only thing that counts is the parts of the cubes that don’t share boundaries, which is simply the 27/ //::46 7? . ! M— / - //(X.y,2); X yZ J 35 )(Hx/ZL? Z; O / FLUK://FI/Vd5- ,_.._ //j’/Z/ﬂ5¢4y//J/§ (M /’o/ I J ”ff/3 Z” :4 j / 7] (056 46 d 7??— ...
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