What actually is a differential? - Mathematics Stack Exchange I am a bit confused about differentials, and this is probably partly due to what I find to be a rather confusing teaching approach (I know there are a bunch of similar questions around, but none o
What exactly is a differential? - Mathematics Stack Exchange The right question is not "What is a differential?" but "How do differentials behave?" Let me explain this by way of an analogy Suppose I teach you all the rules for adding and multiplying rational numbers Then you ask me "But what are the rational numbers?" The answer is: They are anything that obeys those rules Now in order for that to make sense, we have to know that there's at least
Differential algebra and differential-algebraic equations A differential algebraic system of equations is a system of equations where some equations are algebraic equations and some are differential equations The equations need not be polynomial
real analysis - Rigorous definition of differential - Mathematics . . . What bothers me is this definition is completely circular I mean we are defining differential by differential itself Can we define differential more precisely and rigorously? P S Is it possible to define differential simply as the limit of a difference as the difference approaches zero?: $$\mathrm {d}x= \lim_ {\Delta x \to 0}\Delta x$$ Thank you in advance
The logic subtlety behind solving differential equations. The basic logic of solving ordinary differential equations is then that to derive certain conditonal equations from a starting equation, where the conditions are imposed on the domain of the variables, the slogan being: “If I start with something that looks like this here, I also end up with something that looks like this there ” and