# Questions tagged [applications]

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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### Invertible polynomial that approaches linearity at large x

I need to approximate a function $y=f(x)$ using a small set of constants $a_0…a_n$, ideally where the number of constants can be arbitrarily increased to improve accuracy. $x$ and $y$ are both real ...
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### Is there any theorem that can only be proven using the axiom of choice and that is actually used in real-world applications?

I don't have a strong background in mathematics but I am interested in it from a philosophical perspective and I was wondering: is there any theorem or mathematical tool that is used in real-world ...
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### Find a function

It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep and ...
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### Practical application for linear transformations

Can anyone help me with a practical application of linear transformations? I am very curious about how can be an application in real life that can be solved with a linear transformation.
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### How Singular Integrals Theory is applied on Partial Differential Equations

Currently I'm interested in Singular Integrals Theory (I'm a beginner). I have read that this theory has deep relations with PDE's. For that reason I would like to know if there exists some web page, ...
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### Is gaining enough understanding of SVD/QR factorization until you have their formulas memorized useful?

Is knowing how to compute SVD/QRfactorization,Power iteration/power method by hand without notes useful in applications such as Statistics? Now adays, we can do everytime by Mathematica/computer ...
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### Nowcasting, what is it?

I stumbled upon this word in the context of corona virus forecasting. As far as I understand it is some kind of extrapolation method that is also used in economics and meteorolgy, but am struggling ...
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### Application of PDE for solving steady state heat problem.

A thin rectangular homogeneous thermally conducting plate occupies the region $0 \leq x \leq a$, $0 \leq y \leq b$. The edge $y = 0$ is held at temperature $Tx(x − a)$, where T is a constant and the ...
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### Leveraging pure math knowledge to learn applied math

The long and short of this questions is that I’m someone with a pure mathematics background (albeit at a junior-undergrad level) who wants to learn a set of applied math topics in a way leverages what ...
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### First class mathematics that is useful

In Oksendal's Stochastic Differential Equations he writes in the first few pages: The Kalman-Bucy filter is an example of a recent mathematical discovery that has proved to be useful - it is not just ...
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### Area and Volumes of revolution using disc method

(1) The disk method to determine the volume of revolution uses the volume of a cylinder of width dx a proof of this involves showing cylinders (disks) above the curve and those below the curve ...
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### Differential Equation Application of Physics-Sliding Block

Where I can I start to solve this question? A block is released with an initial velocity v0 = 20 m/s from the bottom of an inclined plane making an angle of 30◦ with the horizontal. If the constant ...
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### Physical significance of 3rd derivative [duplicate]

I am new to calculus and currently learning differentiation. I understood that the first derivative indicates the slope of the function and the second derivative indicates the rate at which the slope ...
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### Basic ODE story - tank with pumps

Full tank has $500$ liter of water containing $0.2\%$ of salt. One pipe pumps clear water in ($100$ liters per minute) and the other gets the mixture from the tank ($100$ liters per minute too). ...
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### Simple understanding of advanced math

Title might be a bit vague, so I will explain further here. I am compiling a list of examples of how a person may realize some mathematical result is either obvious or unsurprising from the ...