Wikipedia:Reference desk/Archives/Mathematics/2012 October 13

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October 13

Who decide if a mathematical model is valid?

If you have a set of, for example, differential equations and a natural phenomenon, like storms or whatever. Who is to decide that both match? The mathematicians or the specialist in the natural field? OsmanRF34 (talk) 00:24, 13 October 2012 (UTC)

The specialist in the natural field. StuRat (talk) 00:28, 13 October 2012 (UTC)

Either one of them can make an argument, but ultimately the whole world decides. Looie496 (talk) 00:45, 13 October 2012 (UTC)

You might like this AMS Feature Column - Mathematical Modeling. Personally I'm happy withspherical cows ;-) Dmcq (talk) 10:06, 13 October 2012 (UTC)

A model of natural phenomena like the weather is only a simplification of reality, and you will therefore never get a perfect fit, but a good model will give a very good approximation on variables such as temperature, precipitation, wind, and so on, and thus be a reliable predictor. To test the model, the predictions from the model can be compared to data from actual measurements (these are widely available), and the question becomes whether the proposed model is giving more reliable predictions than the currently used models. New models usually provide a good basis to publish an academic article, this is a major way for scientific results to gain acceptance. Before a journal will accept an article, a team of referees (often two) will scrutinize the model and the article's manuscript to advise the editor on whether this is worthy of publication. These referees may be from a variety of related fields, in the situation you describe, it wouldn't surprise me if an editor would ask both a mathematician and a science specialist to act as referees. Sjakkalle (Check!) 18:50, 13 October 2012 (UTC)

Trigonometric derivatives

The "chain rule" and "inside-outside rule" of derivatives are always messing me up.

what is the derivative, in terms of y, of: sec^2 y' = 1 + y'  ?

Thank you. — Preceding unsigned comment added by Colonel House (talk • contribs) 02:53, 13 October 2012 (UTC)

I wasn't able to figure out what you were trying to do. However thinking about what might be causing you trouble were you trying to do something like for $y=x^{2}$ where $y^{\prime }={\frac {dy}{dx}}=2x$ what is ${\frac {dy\prime }{dy}}$? Dmcq (talk) 10:17, 13 October 2012 (UTC)

Hi! I think ${\frac {dy\prime }{dy}}$ is on the right track. when dealing with this kind of stuff, I think he wants $y'$isolated.--Colonel House (talk) 03:46, 14 October 2012 (UTC)

I still don't know what the question is. If you don't know then ask the person who posed the problem. Dmcq (talk) 20:26, 14 October 2012 (UTC)