Algebraic Operations on Differentials in Liebniz Notation: An Abuse?

[AUMathTutor]

Wow. After having read this thread in its entirety, I can seriously say that I feel substantially stupider for having read it. I condemn everybody who posted to it. Shame on you all.

P.S. If you want to do math with infinitesimals, you should major in physics. Every physics professor I had (a) held mathematics and those who practiced it in general contempt and (b) treated everything as a differential all the time.

 

[Ja4Coltrane]

Yeah, AUMathTutor, you're basically a savior. I am embarrassed for posting here and I accept your condemnation.

I feel so bad for the original poster. His innocent little question should not have led to the least clear, least productive discussion in Physics Forums' history.

 

[Dunkle]

Just curious, why is this thread still here? After all, we don't allow personal theories at this site.

I think I found an answer: http://en.wikipedia.org/wiki/Troll_(Internet)
Although chrisr999 may not intentionally fit this definition, he indubitably does.

 

[snipez90]

Wow. After having read this thread in its entirety, I can seriously say that I feel substantially stupider for having read it. I condemn everybody who posted to it. Shame on you all.

Huh what no, I think I made a valid point somewhere in this thread. I actually forget now, so whatever I guess? Anyways it was tempting to join the discussion but I had to keep reminding myself that I knew what a derivative was and I was pretty sure some of the best explanations took less than 2 pages of a textbook. And for the record, I prefer to think of the derivative as conceptualizing the general notion of the rate of change of a function with respect to a variable. I found some of the geometrical arguments pretty annoying. There is nothing difficult about the notion of the limit of "secant lines". Either way, I'll stick to the precise definitions, since calculus is kind of junk compared to functional analysis.

 

[Phrak]

Umm. I guess someone has to point it out. It was nicely subtle, snipez.

AUMathTutor was being colorful--saying the opposite of what he meant. I'm impressed as well by all of your posts. And I thank you all, as well, guys.

 

[snipez90]

Are you sure you're not being colorful? Actually, in retrospect, I was not the least bit annoyed by any of chrisr999's pedagogy.

 

[Hurkyl]

No Hurkyl,
that is not how i was responding.

Yes, yes it is. If you want to justify "dy/dx is a fraction" by computing difference quotients on the tangent line instead of on the curve itself, then I get to justify "the tangent line is a secant line" by computing secant lines of the tangent line.

 

[chrisr999]

This is a long post, and to be honest it's worth it,
it doesn't matter that it is a very small topic,
atoms are small but not insignificant and look at the trouble there has been about these in terms of nuclear energy and weapons and so on, God help us!
at least this is safe.

of course there will be all kinds of input from all kinds of characters, some not polite but what the heck, if something's worth following, it can be followed to the end.

 

[chrisr999]

Can you imagine finding the geometry annoying!
why is it so difficult to recognise that the math in this case is expressing the geometry in symbolic terms?
Annoyance is an intolerance.
No one is forcing anyone to change their point of view or accept anything they are not prepared to.
When you put things simply that a little kid would understand, it's amazing what responses you can get.

Try some examples.
Differentiate y=(sqrt)(9-x(squared)).
Is your answer recogniseable due to a circle having two tangents for each x or y except at two particular points. Maybe it's better to write the maths using an angle for the variable.

Another one... differentiate x(squared) + y(squared)=0.
why are you dealing with complex numbers?
does it have anything to do with trying to draw a tangent to a circle with a radius of zero?

i don't know lads, you can only flog a dead horse for so long, or can you?

 

[chrisr999]

I might come back to this, but I'm not sure,
to be honest, there's no benefit in operating at the level of some of those last few posts,
this stuff is really simple, basic.
you see the same stuff over and over, there are guys that seem totally intent on making something simple totally confusing for a student trying to learn,
i don't know why they get involved if they can't be contributive.
?

enjoy the pub, lads.

 

[Hurkyl]

Well, I've given this thread far more chances than it deserves, and now it's even degraded to personal attacks with a smattering of political ideology -- there is no point in letting this continue.