3
$\begingroup$

Can one always replace the "big change" (∆) with "small change"(d)? For instance, ∆G=∆H-T∆S to dG=dH- TdS.

Then can I write ∆ as d when the thing in front of it is a differentiable function So that it's infinitesimal change makes sense?

$\endgroup$

closed as off-topic by Claude Leibovici, Ian Miller, choco_addicted, Shailesh, user91500 Apr 6 '16 at 6:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Claude Leibovici, Ian Miller, Shailesh, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.

4
$\begingroup$

The example you posted with "Δ" is Gibbs' Free Energy. However, when we put "d" in it, we get the first law for reversible processes. These are not the same equation, and it's a coincidence they're so similar.

In general, Δ and d mean different things and aren't usually interchangeable.

$\endgroup$
2
$\begingroup$

$\Delta x$ is usually a real number, while the $dx$ in differentiation $\frac{dy}{dx}$ and integration $\int f\,dx$ are not. $dx$ is simply a shorthand for "variable that is integrating with respect to".

The symbol $dx$ follows intuitively from the definition of Riemann sum, (integrating $f$ on $[a,b]$) $$ \lim_{n \to \infty} \sum_{k=0}^{n-1} f(x_k^*) \Delta x = \int_a^b f\,dx $$ but it is only a symbol.

$\endgroup$
2
$\begingroup$

To put it simply, you replace it with $d$, as the change goes to zero.

But you should know that this is a pretty technical object in math, and sometimes there are disagreements by math instructors regarding what $d$ really is, i.e., there are some ways to define what $dx$ or $dt$ is that some mathematicians may not agree with.

$\endgroup$
1
$\begingroup$

Different notations are used for conventions.You may use anything you want as long as you specify the correct meaning of what you are using.

But,try avoiding use of $d$ as $\displaystyle\lim_{x\rightarrow0}∆x=dx$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.