Pushoam
- 961
- 53
Can anyone please tell me significance of these corollaries of fundamental integral theorems?
I can prove these corollaries but I don't understand why do we need to learn it?
Do these corollaries have some physical significance?
(a)$$\iiint_V(\nabla T)d^3 x=\oint_S T d\vec a$$
here S is the surface bounding the volume V .
(b)$$\iiint_V(\nabla \times\vec v)d^3 x= -\oint_S\vec v\times d\vec a$$,where S is the surface bounding the volume V .
(c)$$\iint_S(\nabla T)\times d\vec a =-\oint_P T d\vec l$$ , where P is the boundary of the surface S.
.
I can prove these corollaries but I don't understand why do we need to learn it?
Do these corollaries have some physical significance?
(a)$$\iiint_V(\nabla T)d^3 x=\oint_S T d\vec a$$
here S is the surface bounding the volume V .
(b)$$\iiint_V(\nabla \times\vec v)d^3 x= -\oint_S\vec v\times d\vec a$$,where S is the surface bounding the volume V .
(c)$$\iint_S(\nabla T)\times d\vec a =-\oint_P T d\vec l$$ , where P is the boundary of the surface S.
.