DHS 15.1 - Option 23. 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)

1.23. u (M) = (x - y) z, M1 (1, -5, 0), M2 (3, 7, -2)

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 + 2y + z = 4

3. Calculate the surface integral of the second kind.

 where S - the outer side of the sphere x2 + y2 + z2 = 4

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.

4.23. and (M) = (x + z) i + zj + (2x - y) k, (p): 2x + 2y + z = 4