Recent content by Fu Lin

thank you.:smile:

thanks for reply. I have no idea about general relativity. Could you provide an easy example?

Is it possible to give an example? Say, heat equation, can we change coordinate to come up a mixed derivative term? Or any example to illustrate your idea? thanks

Yes, I mean mixed derivatives both in time and space, like u_{tx} . For example, an equation like u_{t} = u_{tx} + u_{xx}.

The question in short is, why the rank of a matrix is equal to the rank of its transpose? Matrix is an array of numbers. Then it's amazing to me that the number of linear independent rows coincides with the number of linear independent columns. I tried to find some fundamental answer to this...

In pde, it seems to me all kinds of equations about nature phenomena have the property that time and space derivatives are separate. For example, u_t = u_xx, heat equation. So I wonder, is that always the case in nature? I mean, do you guys ever see equation describing real nature mechanism...