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The right question is not what is a differential? but how do differentials behave? Which, as i understand it goes as follows: Let me explain this by way of an analogy
Suppose i teach you all the rules for adding and multiplying rational numbers Can the above definition be brought into consonance with the definition of the differential of a differential form 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. See this answer in quora What is the difference between derivative and differential? In simple words, the rate of change of function is called as a derivative and differential is the actual change of function
We can also define a derivative in terms of differentials as the ratio of differentials of function by the differential of a variable. 69 can someone please informally (but intuitively) explain what differential form mean I am quite new to differential equations and derivatives I want to derive an differential form for equation of an ellipse
If i start with an ordinary ellipse equation \\begin{equation} \\frac{x^2}.
What is difference between implicit and explicit solution of an initial value problem Please explain with example both solutions (implicit and explicit)of same initial value problem 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 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 differential equations class i took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of interesting problems insoluble
2 one could define a linear differential equation as one in which linear combinations of its solutions are also solutions.
Is the above definition of the second differential used today in mathematics This is the question for which i will accept an answer
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