I heard something about the well known Leibniz notation of calculus, and I thought that you guys would be able to tell me if it's a load of hogwash or not.(adsbygoogle = window.adsbygoogle || []).push({});

The geist of it is this: [tex]\mathrm d[/tex] and [tex]\int[/tex] are actually operators, with [tex]\mathrm d[/tex] being an operator that creates an infinitesimal from a variable, and [tex]\int[/tex] being a special kind of summation operator. So, whereas now, we'd recognise [tex]\int \mathrm dx[/tex] as being the same as [tex]\int 1 \mathrm dx[/tex], Leibniz would have seen it as applying an infinitesimal operation to a variable, and then it's inverse.

So, when Leibniz wrote things like [tex]\frac{\mathrm dy}{\mathrm dx}=\frac{\mathrm dy}{\mathrm dt}\cdot \frac{\mathrm dt}{\mathrm dx}[/tex], he saw it as literally cancelling down fractions, not as a trick with limits that just resembles cancelling down fractions.

Is this really what the notation meant? Is it still valid?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Leibniz's operators

**Physics Forums | Science Articles, Homework Help, Discussion**