What are partial derivatives used for in the real world?
describing the rate at which things change relative to the rates at which other things change
>>16258313Economics? Finance?
>>16258314So it always involves more than one rate of change? What use is that? Building spaceships? Agriculture? Chemistry? Is it comparing two rates of change?
Dunks?
>>16258321>Building spaceshipsYes, 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.
>>16258334So does a partial derivative always contain more than one rate of change while a normal derivative is just one rate of change?
>>16258335contains*
>>16258335That 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?
>>16258313Partial 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.>>16258321Partial 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.
>>16258313The partial derivative is just the regular derivative of a multivariate function, when you fix some variables and let only one variable vary.
>>16258363>>16258369You'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.
>>16258375Being part of a differential equation doesn't suddenly change the meaning of 'derivative'.
>>16258344>What field are you up to?No field in particular. I just want to learn math.
>>16258396It kind of does, there's this third path right? Yay! >>16258425Nah. Nobody wants that, only economic guys want that for stats.
>>16258375>>16258437You have no idea what you're talking about. Read a book.
>>16258313Gradient 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.
>>16258313Depends 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 parameterhttps://en.m.wikipedia.org/wiki/Partial_differential_equation#Examples
>>16258313What is addition/multiplication used for in the real world?
>>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.
>>16258602Eeeeeeeh, wat? Lol.
>>16258440Funny you say that. Why do you say that? I don't know.
>>16258636Why do namefags all pretend to be retarded? Is this some weird humiliation kink? An elaborate form of trolling?
>>16258549You should be more gentle.
>>16258313Gradient descent
>>16258313machine learning
>>16258313like everywhere. my god undergrad faggots please go do your homework and stop asking stupid things.
>>16258313physics is pretty much a big fat PDE
the only place I've seen that use almost no PDEs are the sociology trashes and maybe psychology, medicines... even biology use PDEs.
>>16258313With 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.
>>16258319these are by far the worst use cases for partial derivatives
>>16258321Partial derivatives are just the basis decomposition of the gradient.
>>16259982Wrong.
>>16259263hm? what's the best then
>>16258321Thermodynamics for one
>>16262804I feel sick while looking at thisI have a thermodynamics exam on friday
>>16262804dynamics are pretty wasted on thermo.
>>16258321shut up.https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Bellman_equationhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model
>>16258313>Marginal cost in economics>Marginal distribution of a multivariable probability function. >Gradient of a 3 dimensional surface in a particular direction.
>>16260060Elaborate
back propagation on neural networks.
>>16262819It'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.
