DHS 15.1 - Option 1. Decisions Ryabushko AP
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$1.3
1.1. u (M) = x2y + y2z + z2x, M1 (1, -1, 2), M2 (3, 4, -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 + 3y + z = 3
3. Calculate the surface integral of the second kind.
where S - the surface of the paraboloid x = 9 - y2 - z2 (normal vector n which forms an acute angle with the unit vector i), clipping planes x = 0.
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.
4.1. and (M) = 3xi + (y + z) j + (x - z) k, (p): x + 3y + z = 3
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 + 3y + z = 3
3. Calculate the surface integral of the second kind.
where S - the surface of the paraboloid x = 9 - y2 - z2 (normal vector n which forms an acute angle with the unit vector i), clipping planes x = 0.
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.
4.1. and (M) = 3xi + (y + z) j + (x - z) k, (p): x + 3y + z = 3
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