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DHS 15.1 - Option 11. Decisions Ryabushko AP
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Uploaded: 09.11.2016
Content: 11v-IDZ15.1.doc 186 kB
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1. Dana function u (M) = u (x, y, z) and the point M1, M2. Calculate: 1) The derivative of this function in the direction of the point M1 M1M2 vector; 2) grad u (M1)
1.11. u (M) = x / (x2 + y2 + z2), M1 (1, 2, 2), M2 (-3, 2, -1)
2. Calculate the surface integral of the first kind on the surface S, where S - part of the plane (p), cut off by the coordinate planes.
(P): x + 2y + 2z = 2
3. Calculate the surface integral of the second kind.
where S - the outer side of the lower half of the sphere x2 + y2 + z2 = 9.
4. Calculate the flow vector field a (M) through the outer surface of the pyramid formed by plane (p) and the coordinate planes in two ways: a) determination using flow; b) using the formula Ostrogradskii - Gauss.
4.11. and (M) = (y - z) i + (2x + y) j + zk, (p): 2x + y + z = 2
Additional information
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
For the convenience of viewing IDZ solutions on smartphones, an additional file in PDF format is sent
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