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 ...
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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...
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 ...
Proving uniqueness of solution of a differential equation Ask Question Asked 3 months ago Modified 3 months ago
Speaking about ALL differential equations, it is extremely rare to find analytical solutions. Further, simple differential equations made of basic functions usually tend to have ludicrously complic...
Is there a reason it is so rare we can solve differential equations?
2 One could define a linear differential equation as one in which linear combinations of its solutions are also solutions.
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 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 ...