Tutorial#2
Vector Derivatives in Cylindrical Coordinates (Replace s with , everywhere)
Vector Derivatives in Spherical Polar Coordinates
Q 1.
Solution
Q 2. (a) Integrate the div. of v obtained in the previous problem over a volume of the inverted
hemispherical bowl of radius R resting on the xy plane and centred at origin.
(b) Also find out surface integral of v along the surface of the hemispherical bowl specified in
(a).
Check if the two integral are equal. The equality if known as Div. theorem.
Solution
Q 3.
.
(b) Also find out the line integral of T along the path shown in figure below
from (0, 0, 0) to (0, 0, 2).
Solution (a) We know that in spherical polar coordinates
This gives (in the solution below, use T in place of t for the function as given in the question)
(b) Line integral along the given path
Q 4.
(b)
Solution
(b)
Q 5.
Solution
Q 6.
Solution
The Ex. 1.7 here is for Example 1.7. It is given below (done in the class already).
Q 7.
Solution