ИДЗ 15.1 – Вариант 13. Решения Рябушко А.П.

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)

1.13. u (M) = x2 + y2 + z2 - 2xyz, M1 (1, -1, 2), M2 (5, 1, 4)

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): 2x + y + z = 2

3. Calculate the surface integral of the second kind.

 where S - the surface of the paraboloid z = x2 + y2 (normal vector n which forms an obtuse angle with the unit vector k), cut-off plane z = 2.

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.

4.13. and (M) = (x + 2z) i + (y - 3z) j + zk, (p): 3x + 2y + 2z = 6

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