What is the purpose of this symbol?

[TheCanadian]

What exactly is the name and operation of the symbol that is found right after the approximately equal sign in the attachment? I have come across it a lot in readings, and I feel like I should clear up what it is.

 

[micromass]

The imaginary part?

 

[jedishrfu]

What book were you studying? That may give us a clue.

 

[bahamagreen]

The symbol in question is German upper case letter J

On "the approximately equal sign"... watch Carl Bender @ 50:10 - 51:10

 

[pwsnafu]

Dexitify gives $\Im$. German J looks like $\mathfrak{J}$.
Agree with micromass. The imaginary part makes sense contextually as well (approximating the derivative along the imaginary axis).