Recent content by Dimag

Thanks a lot for your help, Diazona. Actually, I am not familiar with methods to solve PDEs. Now, the problem gets reduced to prove the following result: A smooth function f(x,y) fulfills the following equation: \frac{\partial f}{\partial x^2} = \frac{\partial f}{\partial y^2}...

First of all, thanks a lot to JDWood983, AEM and Diazona. Yes, you are right, it is a line integral. Yes, that would be an approach, AEM, but I was given at class a proof using spherical coordinates and I was supposed to give one that does not involve sphercial conversion. Anyway, the...

First of all, thanks for your attention, JDWood983. What I want to prove is that given F a central vector field, then its potential V scalar function, defined as -\nabla V(x,y,z) = F(x,y,z) = - (\frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}, \frac{\partial V}{\partial z}) is...

Homework Statement "Let F be a central vector field, that is, F(x,y,z) = h(x,y,z)(x,y,z) for some smooth function h. Prove that its potential V is radial, i.e., V(x,y,z) = g(\sqrt{x^2 + y^2 + z^2}) for some smooth function g" Homework Equations Since we know that a central vector field must...