Decoding Leibniz notation
I wrote this for myself to understand the Leibniz notation. Prerequisites for this post are the definition of the derivative and the Lagrange notation. If you don’t understand these yet, please study them first.
You may have already seen something like dydx d x d y . This is called the Leibniz notation. The Leibniz notation has many of what Spivak calls “ vagaries”. It has multiple interpretations– formal and informal. The informal interpretation doesn’t map to modern mathematics, but can sometimes be useful (while at other times misleading). The full, unambiguous Leibniz notation is verbose, so in practice people end up taking liberties with it. As a consequence, its meaning must often be discerned from the context.
This flexibility makes the notation very useful in science and engineering, but also makes it difficult to learn. I explore it here to make learning easier.
