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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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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20 views

Interesting/emerging research topics in mathematical modelling? [on hold]

I get the privilege of doing an undergrad research project next year, and I've decided to go in an applied/computational maths route. The problem is, I have no idea where to start and despite looking ...
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2answers
29 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
23 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
22 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
43 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
53 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
53 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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0answers
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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0answers
33 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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0answers
11 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
48 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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0answers
10 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 ...
9
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1answer
157 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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0answers
45 views

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
100 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
22 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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0answers
17 views

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
69 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
147 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
57 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
49 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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0answers
37 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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0answers
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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15 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
49 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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1answer
35 views

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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3answers
41 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
36 views

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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0answers
27 views

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 \...
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1answer
100 views

What's the real life purpose of Knuth arrows?

I recently read about Knuth's Arrows. Didn't even know those operations existed. My questions is: Do they have real-life applications? Most of the times a mathematical development follows a real-life ...
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1answer
9 views

Adding two functions represented by a table of values with a different step size?

Let $f(t)$ be some numerically obtained $T$-periodic function represented by a table of values over one period or a set of points $(t, y)$ with a time step $\Delta t.$ Now let's change the frequency/...
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2answers
38 views

The shortest total length of wire that can be used with a weight.

Suppose a weight is to be held $10 ft$ below a horizontal line $AB$ by a wire in the shape of a $Y$. If the points $A$ and $B$ are $8 ft$ apart, what is the shortest total length of wire that can be ...
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0answers
12 views

Gini Index vs. Revenue for 124,587,000 people and $61,129,151,690,805.40 base

I have a question, given that the gini index is geometrically the ratio between the area enclosed by even income distribution in the United States and actual income distribution, and the area between ...
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3answers
123 views

Why does the Elo rating system work?

The Elo rating system is used to rank players in games such as chess. I can find plenty of explanations online of how to compute someone's Elo rating, how to actually crunch the numbers in practice, ...
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0answers
35 views

What are useful mappings (operators) in image reconstruction

I'd like to ask the technician mates to provide some information regarding mappings and image reconstruction operators. Please, if possible, provide some articles and helpful discussions about useful ...
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2answers
37 views

Probability of survival for system

Consider a system with three identical components and their fault rate is exponentially distributed with $\lambda > 0$. The system needs all three components to function (series system). If you ...
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0answers
37 views

Book recomendation for studying applied Differential Geometry and Topology

What are some good books(or notes in the internet) for (self)studying applied topology and applied differential geometry?
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1answer
56 views

Tropical geometry: practical applications?

In 1960, E. Wigner published a paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Theoretical mathematical structures pave the way to further advances and ...
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1answer
50 views

Fourier Analysis and its applications [duplicate]

My question has two parts: $1)$ Could anyone explain in simple terms what a Fourier Transform is? $2)$ What are some of the applications of Fourier Analysis in the field of high school mathematics?
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0answers
24 views

Applications of Khatri-Rao matrices

I'm interested in what applications there are for Khatri-Rao matrices, and in particular for solving linear systems of equations involving Khatri-Rao matrices. A Khatri-Rao matrix is a block matrix ...
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1answer
52 views

Constant Force Pendulum (undamped)

How does one sketch the derivation of the equation of motion for a planar pendulum of length l and mass m in constant gravity g, subject to a constant torque force F (directed along the tangent to the ...
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0answers
30 views

What are examples of multi-valued mappings in the real world? [closed]

I would like to know about some examples of multi-valued mappings in the real world. Like for example, a function that relates the set of signals emitted by bats and the echo received from nearby ...
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1answer
15 views

Show that if $Q'$ is any point on the line of action of $F$, then $PQ × F$ = $PQ'× F$

If a force $F$ is applied to an object at a point $Q$, then the line through $Q$ parallel to $F$ is called the line of action of the force. We defined the vector moment of $F$ about a point $P$ to be $...
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1answer
47 views

Why do at least half of all random orderings generate a binary space partition of size $n+4n\ln n$ in the random binary space partition algorithm?

Let $S$ be a finite ordered set of non-intersecting finite line segments in the plane. Let's randomly shuffle the elements of $S$ such that each possible permutation of those elements has equal ...
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1answer
31 views

applications of (topological and algebraic) commutative diagrams in organic synthesis

In algebraic topology, there are a lot of commutative diagrams and commutative diagrams up to homotopy. Different ways of compositions of maps in a commutative diagram are equal or homotopy equivalent....
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2answers
61 views

Find the work. Application to physics

A trough in a shape of a semicircular cylinder , is filled with water whose mass density is 1000 $kg/m^3$ . Suppose the water was initially filled to a depth of 3 m. Set up an integral for the work ...