Here’s a handbook of mathematical functions
I’m pretty pissed off about that last one. We used each of those types in engineering, but nobody explained their origins or anything about them. All they said was “this means the derivative too.” wtf?? Why didn’t they say “this was Euclid’s way of writing the derivative”, or “this was Leibniz, and this is why he wrote the derivative this way.
I remember being confused about these different notations and I hated Leibniz notation.
However, now I PREFER Leibniz’s notation because of the idea of the infinitesimal.
Say y = ex and x = cos(W). Then, if we were to find:
dy -- dW
This would be equal to
dy dy dx -- = -- * -- dW dx dW
So you can see its equal visually because the dx’s cancel.
I remember being told that this was something ‘only of a coincidence’, and “they don’t really cancel”.
However, I think Leibniz meant that they did actually cancel, because he saw dx as an infinitesimally small amount.
The idea of the infinitesimal was rejected by mathematicians and apparently replaced by the (more “rigorous”) Epsilon Delta crap that we take in school today.
In the first Calculus course I took, nothing was explained. All they said was “If you have an epsilon, then you have a delta”. It made absolutely no sense. The only way we got marks in that course was by memorizing, not by really understanding.
Why didn’t they talk about the infinitesimal and explain WHY its not used, instead of just totally avoiding it? Its a good concept.