🧵 Untitled Thread
Anonymous at Fri, 28 Jun 2024 16:30:13 UTC No. 16258313
What are partial derivatives used for in the real world?
Anonymous at Fri, 28 Jun 2024 16:31:46 UTC No. 16258314
describing the rate at which things change relative to the rates at which other things change
Anonymous at Fri, 28 Jun 2024 16:34:32 UTC No. 16258319
>>16258313
Economics? Finance?
Anonymous at Fri, 28 Jun 2024 16:35:47 UTC No. 16258321
>>16258314
So it always involves more than one rate of change? What use is that? Building spaceships? Agriculture? Chemistry? Is it comparing two rates of change?
Anonymous at Fri, 28 Jun 2024 16:35:58 UTC No. 16258322
Dunks?
Anonymous at Fri, 28 Jun 2024 16:42:47 UTC No. 16258334
>>16258321
>Building spaceships
Yes, also rocket propulsions and Navi systems, particle acceleration, high-pressure streaming and data compression.
Some say there exists "political science" but they're all derivatives, not really scientific.
Anonymous at Fri, 28 Jun 2024 16:44:26 UTC No. 16258335
>>16258334
So does a partial derivative always contain more than one rate of change while a normal derivative is just one rate of change?
Anonymous at Fri, 28 Jun 2024 16:45:27 UTC No. 16258337
>>16258335
contains*
Anonymous at Fri, 28 Jun 2024 16:53:54 UTC No. 16258344
>>16258335
That depends. If you can figure out if that variable is indeed in causal relationship to something that arouses from two distinctive sources. That is possible. It is funny enough, that you find those causalities outside of current context.
For example let's say you have a tap. You're only able to press a button to get water, water has a certain temperature, you can find it, unless you figure out that there are two other water pipes joining in the back, that also have a special valve simulating same water pressure always.
But then again you have to reconsider cybernetics model by Mazur and some things about feedbackloops.
What field are you up to?
Anonymous at Fri, 28 Jun 2024 17:14:28 UTC No. 16258363
>>16258313
Partial derivatives are just normal derivatives. Derivatives are used, for example, in calculating the velocity of an object, of finding minima and maxima of functions, in approximating various quantities, of simulating physics.
>>16258321
Partial derivative is one rate of change. It's rate of change of a some function f(x) with respect to x. Typically the function f(x) is g(x, y_i...) for some multivariate function g, but not necessarily.
Anonymous at Fri, 28 Jun 2024 17:17:09 UTC No. 16258369
>>16258313
The partial derivative is just the regular derivative of a multivariate function, when you fix some variables and let only one variable vary.
Anonymous at Fri, 28 Jun 2024 17:27:10 UTC No. 16258375
>>16258363
>>16258369
You're in college, am I right? Nah, derivative is much more than that.
Calc me the derivative of x^y^(e^z) wher z is a derivative of x^y^(e^f) where f is ...
You get the idea.
Anonymous at Fri, 28 Jun 2024 17:40:44 UTC No. 16258396
>>16258375
Being part of a differential equation doesn't suddenly change the meaning of 'derivative'.
Anonymous at Fri, 28 Jun 2024 18:00:08 UTC No. 16258425
>>16258344
>What field are you up to?
No field in particular. I just want to learn math.
Anonymous at Fri, 28 Jun 2024 18:06:05 UTC No. 16258437
>>16258396
It kind of does, there's this third path right? Yay!
>>16258425
Nah. Nobody wants that, only economic guys want that for stats.
Anonymous at Fri, 28 Jun 2024 18:08:36 UTC No. 16258440
>>16258375
>>16258437
You have no idea what you're talking about. Read a book.
Anonymous at Fri, 28 Jun 2024 19:14:38 UTC No. 16258549
>>16258313
Gradient Descent for Machine Learning Algorithms via Linear Regression Modeling, now go back and do your Calc 3 homework you stupid faggot.
Also Maxwell's Equations, jesus christ.
Anonymous at Fri, 28 Jun 2024 19:45:14 UTC No. 16258602
>>16258313
Depends on what you mean by "used for". They certainly show up in every partial differential equation, which arise whenever you're trying to model something that depends on more than one parameter
https://en.m.wikipedia.org/wiki/Par
Anonymous at Fri, 28 Jun 2024 19:49:32 UTC No. 16258610
>>16258313
What is addition/multiplication used for in the real world?
Anonymous at Fri, 28 Jun 2024 19:59:42 UTC No. 16258632
>>16258321
>So it always involves more than one rate of change?
Not always.
[math]\frac{\partial f}{\partial t} = c[/math]
Is still a partial derivative equation, it's just one for which the behavior is relatively straightforward to evaluate.
Partial derivative equations relating the rate at which two things are changing with respect to the same variable, or different rates at which different things are changing with respect to different variables lead to much more interesting behavior (ex. changes in motion that depend on changes in position, orientation, distribution of matter, etc.) and are more useful for describing things we observe, they're also more difficult to solve analytically though.
Prince Evropa at Fri, 28 Jun 2024 20:01:42 UTC No. 16258636
>>16258602
Eeeeeeeh, wat? Lol.
Anonymous at Fri, 28 Jun 2024 20:24:35 UTC No. 16258673
>>16258440
Funny you say that. Why do you say that? I don't know.
Anonymous at Fri, 28 Jun 2024 20:25:02 UTC No. 16258674
>>16258636
Why do namefags all pretend to be retarded? Is this some weird humiliation kink? An elaborate form of trolling?
Anonymous at Fri, 28 Jun 2024 20:25:47 UTC No. 16258675
>>16258549
You should be more gentle.
Anonymous at Fri, 28 Jun 2024 20:28:08 UTC No. 16258677
>>16258313
Gradient descent
Anonymous at Fri, 28 Jun 2024 23:43:02 UTC No. 16258940
>>16258313
machine learning
Anonymous at Fri, 28 Jun 2024 23:48:05 UTC No. 16258954
>>16258313
like everywhere. my god undergrad faggots please go do your homework and stop asking stupid things.
Anonymous at Sat, 29 Jun 2024 00:02:48 UTC No. 16258978
>>16258313
physics is pretty much a big fat PDE
Anonymous at Sat, 29 Jun 2024 00:04:21 UTC No. 16258982
the only place I've seen that use almost no PDEs are the sociology trashes and maybe psychology, medicines... even biology use PDEs.
Anonymous at Sat, 29 Jun 2024 00:20:39 UTC No. 16259011
>>16258313
With a "normal" derivative in a single-variable situation, it simply describes the rate of change of a function.
A partial derivative expresses the rate of change of a given variable, in the direction of the basis vector of that variable.
Partial derivatives are quite useful in calculus and vector calculus, with line integrals, green's theorem, stoke's theorem, maxwell's equations, surface integrals, divergence, curl, flux, and so on.
The divergence of a scalar field denotes the direction in which the scalar field grows fastest. The divergence of a vector-valued function denotes the direction in which a vector field diverges from a point (outward, inward, or none). You can use the former for, for example, finding in which direction the rate of change of temperature in a room is the highest. For the latter, you can use this in a vector field (like gas in a room), to find points of low and high pressure.
There are countless other examples, like finding the work done on a body in a magnetic field, the flow of water through a pipe (modelled using a vector field), heat flux, so on. Flux can practically be applied to anything that "flows", and so, partial derivatives need to be used to describe that flow in 3D-space.
Partial derivatives are also used to investigate if certain physical forces or vector fields are conservative (potential functions), for example gravity.
They are, as already mentioned by very many here, used in statistical learning as well.
Anonymous at Sat, 29 Jun 2024 03:51:14 UTC No. 16259263
>>16258319
these are by far the worst use cases for partial derivatives
Anonymous at Sat, 29 Jun 2024 16:28:36 UTC No. 16259982
>>16258321
Partial derivatives are just the basis decomposition of the gradient.
Anonymous at Sat, 29 Jun 2024 17:33:53 UTC No. 16260060
>>16259982
Wrong.
Anonymous at Sun, 30 Jun 2024 19:28:54 UTC No. 16261773
>>16259263
hm? what's the best then
Anonymous at Mon, 1 Jul 2024 13:33:44 UTC No. 16262804
>>16258321
Thermodynamics for one
Anonymous at Mon, 1 Jul 2024 13:56:58 UTC No. 16262819
>>16262804
I feel sick while looking at this
I have a thermodynamics exam on friday
Anonymous at Mon, 1 Jul 2024 16:20:13 UTC No. 16262962
>>16262804
dynamics are pretty wasted on thermo.
Anonymous at Mon, 1 Jul 2024 16:21:42 UTC No. 16262964
>>16258321
shut up.
https://en.wikipedia.org/wiki/Hamil
https://en.wikipedia.org/wiki/Black
Anonymous at Mon, 1 Jul 2024 16:35:26 UTC No. 16262969
>>16258313
>Marginal cost in economics
>Marginal distribution of a multivariable probability function.
>Gradient of a 3 dimensional surface in a particular direction.
Anonymous at Mon, 1 Jul 2024 17:13:19 UTC No. 16263002
>>16260060
Elaborate
Anonymous at Mon, 1 Jul 2024 17:45:27 UTC No. 16263044
back propagation on neural networks.
Anonymous at Mon, 1 Jul 2024 20:26:03 UTC No. 16263239
>>16262819
It's ok anon, nobody really understands thermodynamics. These are all numbers we made up so the equations we need to predict things work. None of them have any physical meaning.