12
$\begingroup$

I would like to add the phrase "Please do not use this tag for differential equations." as first line to the tag .

Of course, differential equations ARE functional equations, but this is not the way that I have seen "functional equations" used and it corresponds to the way I want to use the tag (I am interested in answering questions on functional equations different from differential equations) and I cannot imagine someone using "functional-equations" to search for differential equations. It also seems to correspond to the use of other tags.

However, I realize that this is a question where I am not sure what other users think, so I want to give you a chance to weigh in.


Examples of questions from last week tagged functional equations:

Solving the differential equation $f'(x)=af(x+b)$,

https://math.stackexchange.com/questions/621696/numerically-solving-delay-differential-equations

How to solve $(f'(x+1)+f'(x-1))f(x)-(f(x+1)+f(x-1))f'(x)=0$


Reaction to answers and comments: You have made me understand why people would reasonably choose these tags. I am not 100% convinced that this is a useful thing, but since the default stance is certainly to let everyone decide on their tags, you have convinced me to do nothing.

$\endgroup$
  • $\begingroup$ I agree that the tag is inappropriate for differential equations questions. Can you give some examples of the functional-equations tag being used for such questions? $\endgroup$ – Alex Becker Dec 31 '13 at 23:35
  • $\begingroup$ @AlexBecker Phira has edited some examples in. $\endgroup$ – Mark S. Jan 1 '14 at 0:17
  • 1
    $\begingroup$ Here is a very well known book Introduction to Functional Differential Equations, which might help to change your mind about this specific question. $\endgroup$ – Artem Jan 2 '14 at 4:39
  • $\begingroup$ Does math.stackexchange.com/questions/633385 also belongs to a DDE question? $\endgroup$ – Harry Peter Jan 11 '14 at 12:51
9
$\begingroup$

At least the questions linked in the OP seem to be about relating values of the function (or its derivatives) at different points of the domain in each instance of the equation.

I think this ought to be enough to make the tag apply to the questions, even if the equation also involves derivatives. A priori, solving them they might need a combination of tools from both areas.

$\endgroup$
  • 3
    $\begingroup$ In particular, the first two are about delay differential equations, which I'm somewhat surprised to see we don't yet have a specific tag for. $\endgroup$ – Ilmari Karonen Jan 1 '14 at 19:02
  • $\begingroup$ @IlmariKaronen: I agree, and created dde. $\endgroup$ – Charles Jan 2 '14 at 17:54
  • 2
    $\begingroup$ @Charles Users are unlikely to know what dde means, though. I suggest delay-differential-eqns as either a synonym or as the name of the tag. $\endgroup$ – Post No Bulls Jan 6 '14 at 4:11
6
$\begingroup$

People should not be searching for/favoriting/subscribing to "functional-equations" to look for Differential Equations. I agree with the Phira's position in the question.

$\endgroup$
2
$\begingroup$

The examples you give (the second excepted) are what I would call functional equations, even if they contain derivatives. Henning Makholm's observation is good: the functional equation contains derivatives, but the relation uses different points in the domain. I have seen problems like those in highschool olympiads, and as a highschool students are concerned, these are not differential equations in the sense university students regard them, but merely functional equations in which derivatives appear.

Examples:

http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2650932&sid=e11ad1db842ea084166ec64a0ff8d007#p2650932

http://www.artofproblemsolving.com/Forum/viewtopic.php?p=816031&sid=e11ad1db842ea084166ec64a0ff8d007#p816031

In my opinion, these remain functional equations (even if they contain derivatives), and even their solutions might only use tricks or other functional equations techniques.

$\endgroup$
  • $\begingroup$ Thanks for the enlightening links. These are sort of "Putnam functional equations". $\endgroup$ – Phira Jan 6 '14 at 22:08

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .