My confusion about ##u## and ##\mu##

[docnet]

TL;DR

Are $u$ and $\mu$ used interchangeably in partial differential equations?

Hi all, I am confused about symbols.

I cannot figure out why my partial differential equations professor writes $u$ and $\mu$ in his lectures. A function $u(x, y)$ turns into $\mu(x, y)$. His homework sets are always typed with $u$. I also think he says MYOO during the lectures so it is not just a strange way to write $u$. He is a Frenchman.

 

[fresh_42]

$u$ and $\mu$ are two very different letters, not only because one is Latin and the other one is Greek, but also because $\mu$ is the Greek $m$. I cannot find any $\mu$ in your photo above, and I think it is more a case of sloppy handwriting than it is a case of interchanging the two. However, there are some conventions: $u$ is normally a function, $\mu$ is either an index or a measure. This means that $\int u\,d\mu$ makes sense. But as with all conventions, this is no rule and everybody can use it in a different way.

 

[pbuk]

@fresh_42 is right - this is sloppy handwriting. The same error can be seen in the 'y' characters, particularly in the last line (the second one in $f(y)$ is almost unrecognisable).

Note that outside a mathematical context the prefix 'micro-' which is properly abbreviated $\mu$ is sometimes represented by a 'u' when limited to characters of the Latin alphabet: 1 min = 60 s = 60,000 ms = 60,000,000 us.