Partial differentiation

[chrisheaven]

Suppose you want to forecast the weather this weekend in Los Angeles. You construct a formula for the temperature as a function of several environmental variables, each of which is not entirely predictable. Now you would like to see how your weather forecast would change as one particular environmental factor changes, holding all the other factors constant. To do this investigation, you would use the concept of a partial derivative...

Let the temperature T depend on variables x and y, T = f(x,y). The rate of change of f with respect to x (holding y constant) is called the partial derivative of f with respect to x and is denoted by fx(x,y). Similarly, the rate of change of f with respect to y is called the partial derivative of f with respect to y and is denoted by fy(x,y).

Any comments would be appreciated--- I am trying to post more sensible threads these days LOL

 

[milagros317]

You'll need a hell of a lot more than two independent variables for a weather model. 😀

 

[chrisheaven]

Yes- I'm sure -- however--- the basic concept is sound

 

[chrisheaven]

more to come

 

[EBunbury]

Let me know when you figure out how to convince Mother Nature to hold your other variable constant. That's what makes meteorology a challenge, no null or control experiments.

🙂 E. Bunbury

 

[milagros317]

At least we can give Chris credit for raising the mathematical level of the Silly Stuff Forum. 😀

 

[chrisheaven]

thanks

 

[milagros317]

How about a thread on gradients and Lagrange multipliers? 😀
(Just kidding. )

 

[chrisheaven]

Lagrange coming up........................

 

[milagros317]

Actually, that's a fine thread. 😀

 

[chrisheaven]

isn't it-- I am enjoying it too

 

[milagros317]

I believe that the Lagrange thread is your best ever, Chris. 😀

 

[chrisheaven]

I believe that the Lagrange thread is your best ever, Chris. 😀

Really???????????
Surely the ampersand thread was better!

 

[milagros317]

The ampersand thread was one of your worst, actually. 😀

 

[chrisheaven]

...to which I can only reply...
&&&&&&&&&

 

[milagros317]

That is gross.

Instead, you should contemplate the gradient, del. 😀

 

[chrisheaven]

I thought with your birthday being on 17 March( S.Patrick and harps etc on guinness bottles)), you may wish to contemplate the contents of the attached link--- talks about del!http://en.wikipedia.org/wiki/Nabla_symbol

 

[milagros317]

I had known the symbol was called nabla, but not where the name came from. Thanks for the link, Chris. 😀

 

[chrisheaven]

a pleasure

 

[milagros317]

\nabla is the way to get it printed using TeX or LaTeX. 😀