/sci/ - Science & Math

>>7122824

>>6894899
that's a misconception. most things in physics aren't quantized. Or at least can be modeled by smooth functions
moving around differentials can lead to trouble.

The infinitesimal approach to variational calculus is unintuitive and a bit hand wavy to me.
So I started studying analysis.

Mandatory (actually, I should mention, we can avoid xkcd, my friend's seen all of those, though if anyone's unfamiliar, post away - you're missing out if you've not read it).

I'm taking pchem this year and it's kind of frustrating. Not because it's a difficult class -- it's actually quite easy as far as testing and homework -- but because it all seems unintuitive.

For example, in this homework assignment we're supposed to calculate the differences between Cp and Cv for water at 25C. Which involves about a page and a half of converting and equating partial differentials.

The lectures don't really go over where any of these terms come from and Wikipedia seems to do the same:

http://en.wikipedia.org/wiki/Compressibility

Are these just experimentally found to be true, or what? Can someone suggest a good book or information source about this subject (thermo in particular)?

>>6070494
It also doesn't help that in the sciences people perceive math differently than mathematicians do and this pisses off mathematicians to no end (even the way science people pose their questions pisses off mathematicians).

>We have to know so much math in physics/comp-sci/etc..
>Are mathematics a science?
>Mathematics depend on the laws of matter/biology/nature/etc..
>Why don't mathematicians only study useful things?
>What are some real world applications for x branch of mathematics?

Also, math people argue against math people on points of little consequence. Including the example you posted (in the real world people would just say "it depends").

>Is multiplication just sophisticated addition?
>Does the set of natural numbers contain 0?
>Are mathematics invented or discovered?
>Does the set of real numbers even exist?
>etc..

You never actually see mathematicians arguing about actual math.

>>6040552

Thing is that there's some special things that only work in specific cases but not the general case. The specific cases are often not as interesting to mathematicians because they can't be generalized.

>who cares if you can prove something ridiculous for an equally ridiculous ring, it doesn't generalize to any other rings

pic somewhat related

>yfw

Most non mathematicians think, that infinitesimals have multiplicative inverses and that canceling out a dx is not a big deal.
Sometimes it doesn't work.
That's why "physicist substitutions" make me cringe even if they work most of the time

>the Dirac delta is not a function they said
>use it as it if were one anyway