/sci/ - Science & Math

>>9951231
It's the limit of a ratio

>>9951231
not an argument

Leibniz notation is something so retarded only physishits use it unironically.

>>9951231
Did you actually feel this needed explaining? What are you compensating for?

>>9951268
he's probably learning derivatives in class and some kid next to him said "hurr cancel out the d and solve for x"

>>9951244
HAHAHAA this

>>9951275
/thread

>>9951244
i mean i fucking hate physhitards

>>9951231
You can sometimes (almost all times in most college calculus problems?) informally treat it as a ratio though, and doing so results in "nice" results

I never took real analysis which I believe is the "formal" version mathematicians take, but I did take all of the advanced statistics and probabilities that economists must take, and I know a similar thing happens where even the informal stats most engineers take are pretty goddamn robust.

Ratios can be operators too though

>>9951268
op btfo
sage
>>9951231
No shit underage sherlock.

>>9951231
True enlightenment is rigorously proving that this quick and dirty notation works when solving for basic ODE's as a 3 minute aside.

That's what my differential equations professor did.

>>9951295
Correct anon, it has to do with differential forms and measures. Sometimes we can treat such objects algebraically, sometimes we cannot.

>>9951374
This ffs. It takes no time to prove a lot of the shit you use, and so the abuse of notation is justified.

>>9951374
lucky you, my differential equations professor was banned by the department from writing his own exams after our first midterm

>>9951449
whoa. story?

>>9951374
>rigorously proving that this quick and dirty notation works when solving for basic ODE's
Link me more

>>9951494
https://math.stackexchange.com/questions/2142783/separable-differential-equations-detaching-dy-dx

The second answer
Basically as long as g(y) is continuous/integrable in x, and you track when you divide out solutions, you can use this shortcut for equations that are separable. Think about it using chain rule

>>9951494
Its called change of variable theorem brainlet.

>>9951231
>This is not a ratio and if you treat it as a ratio, you are wrong.
The derivative is indeed a ratio of differentials. It directly follows from the definition of the differential as principal linear part of the increment of the function. For proof, see Zorich, for example.

>>9951231
If it's stupid but it works - it isn't stupid.

>>9951244
Great bait

>>9952004

>>9951231
It's a tensor Dᵗˣfₓ = δ'(t - x) f(x) I think?

>>9953502
Yes, but in the same sense that any linear map between vector spaces is also a tensor.

>>9951374
My differential equations professor just told us not to go near pure mathematicians.

But you can pretend it is and most of the time it just werks

>>9951244
real physicist use a dot on the variable

>>9951231
Does it really matter [eqn]what[/eqn] it is?

>>9954441
Get a load of this undergrad