DHS 15.1 - Option 3. 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)

1.3. u (M) = ln (x2 + y2 + z2), M1 (-1, 2, 1), M2 (3, 1, -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): 3x + 3y + z = 3

3. Calculate the surface integral of the second kind.

 where S - the outer side surface of the cube bounded by the planes x = 0, y = 0, z = 0, x = 1, y = 1, z = 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.

4.3. and (M) = xi + (x + z) j + (y + z) k, (p): 3x + 3y + z = 3