4 ms·
Interesting! This same problem occurs in calculus as well. Leibniz's notation is pretty offensive, for example: in basic calculus, d/dx is an operator. In diffe
by gcv 14y ago
Interesting! This same problem occurs in calculus as well. Leibniz's notation is pretty offensive, for example: in basic calculus, d/dx is an operator. In differential equations, you suddenly begin treating dx as a separable algebraic term — and way too many teachers suck at explaining why this is suddenly permissible.
- sanxiyn 14y agoI recommend Elementary Calculus: An Infinitesimal Approach to those interested in calculus. It treats dx as a term from the start, and matches my (and I suspect most people's) intuition of the subject much better than epsilon-delta. And it is actually completely rigorous, not hand-waving infinitesimals.
- vlad 14y agoThe book is available as a free online pdf: http://www.math.wisc.edu/~keisler/calc.html http://www.math.wisc.edu/~keisler/calc.html Checking it out now.
- gizmo686 14y agoMy high school has a relatively progressive math program, and we never learned d/dx as a function. We began calculus with limits, then started solving Lim[dx->0](dy/dx), then we started using d/dx as a shorthand so we did not need to pull a nested expression out to take its derivative. I never thought to think of d/dx as a function until I started doing functional programming.