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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Applications of Topological Complexity of configuration space

I'm starting to work on Topological Complexity of configuration spaces . Articles say that it has applications in robotic and control theory . My questions are : 1) How Topological complexity can help ...
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1answer
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A problem of Tangents on curvers

Let $X=\phi(x,y)$, $Y=\psi(x,y)$ define a transformation of the $xy$-plane to $XY$-plane. Suppose further, $\phi_x=\psi_y$ and $\phi_y=-\psi_x$. Then prove that the angle between the curves $F(x,y)=0$ ...
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1answer
45 views

Critical Number real life applications

I've studying a lot Critical Number/Point and I have to give a presentation about it. I am searching real life applications to explain the concept, but it's difficult to find. Anyone here can give ...
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3answers
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The value of an investment in Canada Savings Bonds is modelled by $A(t) = A_0 e^{0.0255t}$… Rest of question below.

The value of an investment in Canada Savings Bonds is modeled by $$A(t) = A_0 e^{0.0255t}$$, where A is the amount the investment is worth after $t$ years, and $A_0$ is the initial amount invested. At ...
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30 views

Invertible product of noninvertible morphisms

This question may be too broad. Under what conditions is a product of noninvertible morphisms invertible? Suppose that we model a finite number of different acts of observation (i.e., a thermometer ...
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13 views

How to find (GEV) distribution parameters with optimization?

I'm currently trying to replicate this study with python. http://pages.stern.nyu.edu/~sfiglews/Docs/RND_draft7.pdf The section I'm currently working on is between p.17-20 in the study. The study ...
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3answers
665 views

Where do you see cyclic quadrilaterals in real life?

I've just been studying cyclic quads in geometry at school and I'm thinking see seems pretty interesting, but where would I actually find these in the real world? They seem pretty useless to me...
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36 views

Does anyone recognise this non-linear diffusion equation?

I'm doing some work on modelling cell migration, I've derived this particular form of a non-linear diffusion equation to describe the mean behaviour of a stochastic model I'm studying. I was wondering ...
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49 views

How to find the system transfer function corresponding to a two dimensional matrix of optical transfer functions?

I would like to find the system transfer function corresponding to a two dimensional matrix of optical transfer function where: Each of the 3 times 5 = 15 interferometers produce 15 sets of ...
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1answer
99 views

Advanced Linear Algebra vs Functional Analysis

I have a couple questions regarding Advanced Linear Algebra vs Functional Analysis. 1) Do these courses help in understanding or have applications in: Machine Learning Quantitative Finance, ...
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15 views

Luminosity and Apparent flux

The stars in our Galaxy have luminosities ranging from $L_{\text{min}}$ to $L_{\text{max}}$. Suppose that the number of stars per unit volume with luminosities in the range of $L$, $L+dL$ is $n(L)dL$. ...
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22 views

Polynomial Chaos with Beta Distribution - Standard Beta Random Variable, Transformation of Beta Random Variable

Background: I am dealing with a non-intrusive polynomial chaos expansion (e.g. here [Hosder,Walters;2010]). This means I want to represent an uncertain output $U(\xi)$, dependent on a vector of ...
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53 views

Where is number theory used in programming? [closed]

I'm developing corporate software (for banks, insurance companies, hospitals and so on), and I am interested in number theory. I am a beginner in this area and I understand most of the theorems and ...
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2answers
31 views

Application of Chain Rule for Paths

I'm a graduate student and I'm currently teaching multivariable calculus. I gave my students a question about a bug traveling along a circle of radius $200$cm in the $xy$-plane. We suppose also that ...
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3answers
51 views

How to prove $A\cos(\omega t-\phi)$ = $a\cos(\omega t)$ + $b\sin(\omega t)$ using $e^{i\theta}$?

I want to show that $A\cos\left(\omega t-\phi\right)$ = $a\cos\left(\omega t\right)$ + $b\sin\left(\omega t\right)$ First I verified for myself through the angle addition proof that: $$ \cos\left(\...
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3answers
74 views

Splitting a file into $m$ pieces of size $1/n$, such that any $n$ pieces allow you to recover the file?

Let's say we have a file (which we could define as a finite sequence of 0's and 1's (or any other two symbols)). For $m > n$, can you create $m$ pieces (which are themselves files), each $\frac 1n$...
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3answers
188 views

What are the most obscure or advanced mathematics with practical application

Throughout my engineering studies there were jokes made by my professors (mostly mathematics professors) that referenced the fact that pure mathematicians strive to create mathematics with no ...
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70 views

How might an applied mathematician view $ 1/x$, $\ln x$, and $e^x$?

I understand that the natural logarithm was developed by Gregoire de Saint-Vincent and Alphonse Antonio de Sarasa as to represent the area under the curve of the hyperbola $\frac1x$ before the ...
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2answers
39 views

Well Defined Applications

Let $H$ be a subgroup of $\textrm{Isom}(\mathbb{R^n})$ And let $O(n)$ be the orthogonal group. Let $T_v$ be the translation by $v$. If we have the following application : $\Phi : H \rightarrow O(n)$ ...
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Future learning for a math graduate in applied mathematics references

As a mathematics graduate with focus on programming we did a whole lot of coding of some mathematical statements (as well as proving them), but yet rarely giving real life examples and applications ...
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2answers
33 views

Marginal revenue of a monopolist [closed]

A monopolist faces a demand function $Q=4000(p+7)^{-2}$. If she charges a price of p, her marginal revenue will be: (a) $p/2+ 7$ (b) $2p+ 3.50$ (c) $p/2-7/2$ (d) $-2(p+7)^{-3}$ Correct answer is ...
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1answer
24 views

Production functions total cost

Production function is: $f(L,M)=L^{1/2}M^{1/2}$. L is the number of units of labour, M of machines used. Cost of labour is 9 per unit, whereas the cost of machine is 81 per unit. Total cost of ...
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1answer
25 views

Motion and differentiation

Two particles A and B start from the origin at the same time and move along a straight line so that their velocities in m/s at any time t seconds are given by: V$a$ = $t^2 + 2$ and V$b$ = $8- 2t$ a. ...
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1answer
47 views

What are some applied math projects/research Ideas that i could do over the summer

I am a high school senior and before I leave for college I want to learn the process of doing applied mathematics. I am having trouble with coming up with ideas. I know through multivariate/vector ...
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1answer
54 views

Exponential growth and decay question [closed]

A city has a growing population at a rate proportional to the current population, that is: $$\frac{dP}{dx}=kP.$$ Verify that $P(t)=P_0e^{kt}$, $t>0$ is a solution of the equation. If the ...
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1answer
56 views

What are practical applications of infinite products?

My analysis book covers a section on infinite products. So I started wondering what the practical applications of infinite products are in science and engineering, but couldn't find anything yet. Also,...
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8 views

Function to represent discrete forces

I am trying to describe the force exerted by the two wheels of a 2d model of a car (one wheel in front of another) each with a magnitude of $F$. Is there any function I could use besides a piecewise ...
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34 views

What does it mean: “Strings of Constraints” [closed]

I am reading an article in the field of applied mathematics. I've ran into a sentence that reads: The string-averaging algorithm projects a point sequentially along several independent strings ...
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12 views

A formular for supply and demand for a simple computer game

I'm making a game where there is a market where the price is affected by supply and demand. This is so that there are diminishing returns as the play dumps lots of the same goods on the market and ...
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1answer
50 views

How can one tell if a PDE describes wave behaviour?

I have been looking at a lot of different non-linear PDEs which describe waves lately and have come to the realisation that I don't know what it is about these PDEs that make them behave like waves. ...
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12 views

Bounds on the divisor of Webster's apportionment method

I am currently in the process of studying various apportionment methods in a summer class, and while learning about Webster's apportionment method (also known as Webster-Willcox or method of major ...
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1answer
165 views

Application of Combinatorics/Graph Theory to Organic Chemistry?

Recently, I have been self-teaching graph theory and having an organic chemistry course at school. When I was learning isomer enumeration I found great resemblance between organic molecules and ...
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If a x b = a x c. What is the relationship between b and c? [closed]

This is a question on my worksheet and what I've written down so far is we have vectors $\vec a\ne0$ and $\vec b,\vec c$ such that: $\vec a \times \vec b = \vec a \times \vec c$, and I have to find ...
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5answers
101 views

Applications of $f(x_0)=f'(x_0)$

If a function $f(x)$ has a derivative $f'(x)$ then where $f'(x_0) = 0$ there is an extreme point at $x=x_0$. And where $f''(x_0)=0$ there is an inflection point at $x=x_0$. I am asking are there any ...
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1answer
23 views

Showing complex transformations in a fluid way

It says it all in the title: I need to show how simple complex transformations (translations and dilations, or even both) affect shapes on the complex plane in a "fluid" way – that is, creating some ...
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Minimal and maximal problem

Cuboid with contlstant volume $V$ its base is a rectangle length $nX$, width $X$ The whole area of cuboid is $A$ and $A$ was minimal area Prove with differentiation that $A^3n=54 V^2(1+n)^2$
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4answers
72 views

Mathematics for Guidance, navigation and control

I'm finishing my math degree this week and have been looking for some subject to practice and study on my own while I'm doing some work as a programmer. I'm interested in getting my master's later but ...
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1answer
37 views

Where i am going wrong in finding normal to curve?

The question is Find the perpendicular distance between the normal to the curve $$x=a\cos t+at\sin t, y=a\sin t-at\cos t$$ and the origin. Equation is given in parameterized form. My attempt ...
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1answer
148 views

Which numbers are necessary?

The Greeks were initially convinced that all numbers were rational until upon pain of contradiction were forced to accept that $\sqrt{2}$ was irrational and needed to be included in our number system ...
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1answer
69 views

What practical purpose — or application — do directrices serve?

In Calculus II (and briefly in Trigonometry, if I remember correctly) the concept of a directrix began poking its head around conic sections. While covering parabolas, ellipses, and hyperbolas, the ...
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1answer
64 views

Applications of the wave equation

I've recently started to take interest in PDEs and how to solve them, and I'm wondering a bit about real life applications of the wave equation. So far I haven't found anything about practical ...
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38 views

mathematical terms with fractions and variables - usage in daily life?

what usage do algebraic fractions (monomial or polynomial) have in our life? Are there specific professions that deal with them now and then? Where exactly in technology do they have their very own ...
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31 views

Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... $$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
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23 views

Applications of Integration - Work Done by a Variable Force

Question states: "A 20-foot chain weighting 5 pounds per foot is lying coiled on the ground. How much work is required to raise one end of the chain to a height of 20 feet so that it is fully ...
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16 views

application of integration in graphics

Is Integration used in animation/computer graphics? If yes, then how it is used. A couple of example would be great . Thanks
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1answer
52 views

Area bounded by$ y^2=x^2(1-x^2)$

Find the area bounded by $y^2=x^2(1-x^2)$? I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
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Find the volume obtained by totating the area formed by $y=x$ and $y=\sqrt{x}$ about $y=1$

The questions asks us to find the volume of solid formed when the area between $y=x$ and $y=\sqrt{x}$ is rotated about the line $y=1$. I understand that a cone is formed. Now, to find the volume, I ...
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50 views

Practical examples of tank mixing problems?

In calculus and differential equations, a standard example of word problems are mixing problems, with some number of tanks, and brine often being an output of the system. With one tank, I can imagine ...
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1answer
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Unique solution for circuits in Linear Algebra

A standard application of Linear Algebra is circuits and Kirchhoff's Laws. Does anyone know of a proof of uniqueness of a solution of a system given by these laws? There are many, many examples, but ...
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Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a \...