- #1
kliang1234
- 13
- 0
Hi, this is a very simple question about the curl theorem. It says in my book:
" If F is a vector field defined on all R3 whose component functions have continuous partial derivatives and curl F = 0 , then F is a conservative vector field"
I might sound stupid, but what exactly does "defined on all R3" and "continuous partial derivatives" mean? Can you also provide examples?
I tried to apply it to a problem:
If Curl <0, z/(z^2 + y^2) , -y/(z^2+y^2) > = 0 , is the vector field conservative?
The answer is no. Can anyone explain why its not conservative.
It is continuously differentiable, and curl F = 0. To me, it appears to satisfy the criteria of the theorem.
Please help, i have a midterm tomorrow.
" If F is a vector field defined on all R3 whose component functions have continuous partial derivatives and curl F = 0 , then F is a conservative vector field"
I might sound stupid, but what exactly does "defined on all R3" and "continuous partial derivatives" mean? Can you also provide examples?
I tried to apply it to a problem:
If Curl <0, z/(z^2 + y^2) , -y/(z^2+y^2) > = 0 , is the vector field conservative?
The answer is no. Can anyone explain why its not conservative.
It is continuously differentiable, and curl F = 0. To me, it appears to satisfy the criteria of the theorem.
Please help, i have a midterm tomorrow.