DHS 15.1 - Option 19. Decisions Ryabushko AP

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DHS 15.1 - Option 19. Decisions Ryabushko AP

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)

1.19. u (M) = 3x2yz3, M1 (-2, -3, 1), M2 (5, -2, 0)

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 - y + z = 2

3. Calculate the surface integral of the second kind.

 where S - the surface of the cone x2 + z2 = y2 (normal vector n which forms an obtuse angle with the unit vector j), clipping plane y = 0, y = 1.

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.

4.19. and (M) = (2x - z) i + (y - x) j + (x + 2z) k, (p): x - 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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