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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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Swaying string, a question regarding the derivation of formula

In my textbook, with $S=|\mathbf{S}|$, from the picture below, they derive $\int_{x}^{x+h}\rho_lu_{tt}''d\lambda=S(x+h)\sin(\alpha(x+h))- S(x)\sin(\alpha(x))+\int_{x}^{x+h}Fd\lambda$, where $F$ is [...
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1answer
25 views

Which logistic equation is better for solving this question?

So I was given a question about spread of disease: A virus is spreading through a city of 50,000 people who take no precautions. The virus was brought to the town by 100 people and it was found ...
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0answers
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Appropriate test for biological data [closed]

So I did a test to see how much an insect is attracted to a smell. It was done for three scents (and repeated thrice). Test tubes were marked into 4 sections and then the number of flies in each ...
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8answers
840 views

Practical application of matrices and determinants

I have learned recently about matrices and determinants and also about the geometrical interpretations, i.e, how the matrix is used for linear transformations and how determinants tell us about area/...
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1answer
44 views

Equations or areas where $(AA^T)^x$ or $(A^TA)^x$ are used as applications

Let $A$ be square or rectangular and $x\in \mathbb{R}$. Can you point me to equations/areas out there where $(AA^T)^x$ or $(A^TA)^x$ or their eigenvalues are used as applications? e.g. we find them in ...
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6answers
314 views

Importance of differentiation [duplicate]

I have just started learning about differentiation. I know that differentiation is about finding the slopes of curves of functions and etc. I have many saying that differential and integral calculus ...
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1answer
29 views

Find a homeomorphism

Let $X=A\cup B \cup C$ where $A=\{(x,y) :(x+2)^2 +y^2 =1\}$ and $B=\{x^2+y^2 \leq 1\}$ and $C=\{(x,y) :(x-2)^2 +y^2 =1\}$. Find a homeomorphism between the quotient space $X/B$ and $E=\{(x,y) :(x-1)^...
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48 views

real world applications of direct sums

I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was ...
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1answer
35 views

Surface area of a sphere over a disc

What's the surface area of the sphere $x^2 + y^2 + z^2 = 1$ over the disc $(x-1/2)^2 + y^2 \le 1/4$ ? I've tried something, but I don't think it's right, as it's not a "nice answer" So here is what ...
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1answer
72 views

Is curvature a tensor? The curvature of a metal roof per example

Reading adout the egregium theorem and the way it is applied in structural engineering I met the preposition that curvatures are tensors which I don't understand. Tensors relate vectors with other ...
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3answers
155 views

Applications of “finite mathematics” to physics

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias. When I think of applications of maths outside of itself, I ...
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0answers
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How is it possible a ruled surface to be composed of straight lines?

And a double ruled surface is composed of two groups of straight lines. This is what gives to this shape its exceptional resistance to buckling How is it possible a curved surface to be composed of ...
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0answers
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Probability of stripes being distinguishable given probability density functions for each luminance

I have an image with seven stripes on it (or three stripes on a dark background), and the goal is to estimate the probability of whether they are distinguishable from one another. If the values of ...
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1answer
17 views

Disagreeing methods for computing pregnancy probabilities

Something that I would have thought to be dead simple nearly drove me crazy! Let's say we make a small study of women who have similar factors for becoming pregnant. Let's say the study runs for two ...
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1answer
31 views

Are there applications of equivalent matrices?

Similar to the definition here, matrices $A$, $B$ $\in \mathbb{C}^{m\times n}$ are said to be equivalent if there exist some invertible $m\times m$ matrix $P$ and some invertible $n\times n$ matrix $Q$...
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1answer
16 views

Differentiated - Rates of change

A triangle $ABC$ is made out of an elastic piece of string. Vertices A and B are being pulled apart so that the length of the base $AB$ is increasing at of $3 \ cm \ s^{-1}$ and the height $h$ is ...
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0answers
35 views

“Work done” my a muscle during weight-lifting

I'm looking for a simplistic way to describe the "work" done by muscles during compound weightlifting movements. Perhaps not work in the precise physics sense, but an overall idea of how much the ...
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1answer
29 views

Purpose of rotation of a Function or Graph

You are able to rotate any function by an arbitrary angle around the origin using the formula, $$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, ...
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0answers
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Area transformation

I have two rows of different types A and B. Every row is of the size 1$\times$N, where every element can be either 1 or -1. If we consider a single row of type A={-1,1,1,1,-1,1,-1,...} of size 1$\...
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0answers
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R²/Plane Subset Equation With Plane Homothetic Transformation

Let's consider $H_k∶\ \left\{\begin{matrix}\mathbb{R}^2\rightarrow\mathbb{R}^2\\(x,y)\longmapsto(kx,ky)\\\end{matrix}\right.\ $. It is an homothetic transformation of $\mathbb{R}^2$ of center $(0,0)$...
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2answers
55 views

Find if the function $\frac{(1-2xy)}{(x^2 +y^2)}$ has a max or min value for $(x,y)=/=(0,0)$

Does the function $\frac{1-2xy}{x^2 +y^2}$ have a max or min value for $(x,y)=/=0$? What I've tried so far is to take the the partial derivatives: $$\frac{\partial f}{\partial x} = \frac{2(-x+x^2*y ...
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0answers
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Derivation of 2D Korteweg-de-Vries equation

Coming from engineering rather than mathematics, I am recently dealing with non-linear partial differential equations e.g. like the well known Korteweg-de-Vries equation: $$u_{t} + uu_x + u_{xxx} = 0$$...
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1answer
37 views

Bernoulli differential equation applications? [closed]

Just like the title states, I’m interested in practical applications of Bernoulli differential equations.
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0answers
14 views

Intersection of isometries of a polygon

Suppose we have a two dimensional polygon $P$. And a sequence of polygons $(P_i)$, where each $P_{i+1}$ is a small translation/rotation of $P_i$. I am interested in situations where $\cap P_i$ is ...
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2answers
44 views

Optimal time for three people to travel

Three men need to travel 60 km. They have a motorbike that can travel at 50 km/h but only two people can fit on it. They can walk at a speed of 5km/h. Can they get to their destination in 3 hours? I ...
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0answers
28 views

Recommended knowledge for Applied Math

I would like to know which topics below are important for applied math and why? If you know about only one subject, share your answer with me please. Topology Set Theory Linear Algebra Abstract ...
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1answer
26 views

Application of logs

The number of milligrams, $d$, of a drug remaining in a patient's bloodstream, $t$ hours after it has been administered, is given by the equation $d = 5(2.7^{.04t})$. To the nearest minute, how long ...
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0answers
6 views

Do there exist discrete and self-orthogonal wavelets on non-cartesian grids?

Most 2D DWT:s that I know about are rather straight-forward separable 1D wavelets, for example Meyer, Daubechies famous maxflat, CDF as used in JPEG-2000, spline wavelets like Unser's and so on. Has ...
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1answer
24 views

Could families of “Airys” and “Bairys” of integer “frequencies” be useful?

A very famous family of functions are the complex exponentials and in the case of real valued functions, the sin and cos functions. They are related by the famous Euler formulas: $$\exp(i\phi) = \cos(...
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0answers
99 views

Understanding a function space

I was reading a paper on Homogenization theory, where the author uses the spaces of vector valued functions. Let us consider such a space $D[\Omega; C^\infty_P(Y)]$, consisting of all the compactly ...
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3answers
80 views

What are some applications of subdirect product?

I have studied direct products. I know a few applications of direct products, like group isomorphism, etc. What are some applications of sub-direct product of groups?
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The importance of estimates of frame bounds.

A theorem contained in Christensen, Ole (1995), "A Paley-Wiener theorem for frames." Proceedings of the American Mathematical Society, 123, 2199-2201. states that Let $\{x_n\}_{n\in\mathbb Z}...
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1answer
32 views

Closed-form solution for $f(x)/x=y$ using $f^{-1}$

I'm programming a piece of math that requires solving an equation of a form $f(x)/x=y$. Now I already have $f^{-1}(z)$ coded (efficiently, and not by me) so I'd prefer using this implementation ...
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2answers
63 views

Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?

Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...
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1answer
53 views

How do I tell the rank of the electric susceptibility tensor (and others)?

I understand that a tensor is a multilinear map from $V^*\times\cdots\times V^*\times V\times\cdots\times V$ to $V$'s underlying field, where $V$ is a vector space and $V^*$ its dual. This is fine, ...
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1answer
40 views

A collection of lines drawn between points in a regular 13-gon - how to determine where the points sit relative to each other?

So I have 4 collections of lines drawn between points each making a path. The angles are measured. The problem I am attempting to solve is to determine whether or not each of the collections of points ...
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3answers
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What are some applications of mathematics whose objectives are not computations?

In mathematics education, sometimes a teacher may stress that mathematics is not all about computations (and this is probably the main reason why so many people think that plane geometry shall not be ...
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1answer
23 views

Can we solve the functions describing the bend of a cable at rest fixed at two positions?

Assume we have a cable which endpoints is attached to two points at $(x,h)$ and $(x+\Delta_x,h)$. Further assume it has some mass density distribution, $\rho(m),m \in [0,l]$ and is of some length $l ...
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4answers
47 views

How to solve this problem without letting coordinates as $(a \cos\theta , a\sin\theta)$

Q. Tangent to the circle $x^2 + y^2 = a^2$ at any point on it in the first quadrant makes intercepts $OA$ and $OB$ on $x$ and $y$ axes respectively, $O$ being the centre of the circle. Find the ...
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1answer
95 views

Path of a simple turning car?

I am planning to build a small car that needs to travel through three specific points. Obviously, the car will need to travel in a partial circle to do this. In order to do this, I need to calculate ...
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1answer
45 views

Applications of coupled systems of $\;2\times 2\;$ linear differential equations

I am providing maths help to some students studying just before University level in mathematics. I am writing some practice questions for them on solving coupled first order linear equations and I ...
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1answer
47 views

set up triple integral for volume

I was working on practice problems in the textbook and got stuck on this question. Any help would be greatly appreciated. Set up two triple integrals with two different orders of integration that ...
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0answers
36 views

Applications of Riemann surfaces in engineering or physics

I know that the maximal analytic continuation of a holomorphic function is an example of Riemann surfaces but don't know what it is used for. What can we do with this surface?
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1answer
31 views

Is there a right identity for Application in Lambda calculus?

Such a function E that: ∀F (F E = F) It's obviously, that the left identity E' (E' F = F) ...
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2answers
135 views

Is there any “good” definition for what constitutes “applied mathematics”?

Is there any "good" definition for what constitutes "applied mathematics"? Wikipedia lists stuff such as statistics, optimization. However, e.g these have certainly "pure mathematical" aspects to ...
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1answer
28 views

Lagrangian of an equation, a particle with a time dependent constraint

I'm currently studying for an exam and I came across the following question. Consider a bead of mass m constrained to move along a wire which is on the vertical $(x, y)$ plane. The wire has equation $...
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1answer
88 views

Paasche price index: cost of living adjustment (economics)

I am trying to figure out the following question involving the Paasche price index: two goods are perfect substitutes (let's assume for simplicity that indifference curve has slope of -1) relative ...
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0answers
259 views

Real world applications of Riemann surfaces of holomorphic functions [closed]

The maximal analytic continuation of a holomorphic function is an example of Riemann surfaces. What is it used for? Please edit the question to limit it to a specific problem with enough detail ...
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0answers
8 views

Applications for quasi-groups and loops outside of cryptography

I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually ...
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0answers
49 views

Applications of $L_p$ spaces

I'm studying Lebesgue integration theory and understand the definition of $L_p$ spaces. What can we do with $L_p$ spaces?