For questions about ordinary differential equations, which are differential equations involving ordinary derivatives of one or more dependent variables with respect to a single independent variable. For questions specifically concerning partial differential equations, use the [tag:pde] instead.
Does there exist any correspondence between difference equations and differential equations? In particular, can one cast some classes of ODEs into difference equations or vice versa?
As I am progressing differential equations practice, I found myself at somewhat of a roadblock. The roadblock is essentially that let's say we have the following equation:$$\int x^2\,dx=\int y\,dy....
A differential form is (technically) a function that we can calculate value at a point and AFAIK it has nothing to do with infinitesimals nor tends to anything. A course in precalculus, calculus, or even real analysis almost never gives an answer to "What is dx?". It is only until differential geometry, one gets to learn what it is. One should not learn these from Wikipedia but from a ...
derivatives - What is the difference between a differential and a ...
Anyone who sees calculus in application is likely to encounter both derivatives and differentials. The two concepts have confusingly similar notation. For that reason, this post is a very important contribution.
calculus - What is the practical difference between a differential and ...
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 ...