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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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\Delta L_i=\sqrt{(\Delta x_i)^2+(\Delta y_i)^2}=\sqrt{1+\left(\frac{\Delta y_i}{\Delta x_i}\right)^2}\space \...
user1062191
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How to make calculations for a complex 3-D conduit shape?
I'm an electrician running conduit horizontally along a wall at a height of 6 feet off the floor, when I come to a corner of the room. Normally, I would bend a 90-degree elbow and continue level along ...
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Calculus application question
My attempt:
Step 1: Find $x$ in terms of $t$.
$\frac{dt}{dx} = \frac{1}{-0.15x}$
$t = \frac{1}{-0.15}\ln(x) = x^{-1}(t)$
$x(t) = e^{-0.15t}+c$
However, here is where I am stuck. Without any extra ...
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Woodworking: How do I calculate the matching depth of a Vee Bit to a Roundover Bit?
While v-carving with a CNC router, the width of the cut is determined by depth of the Vee bit in the material. Simply stated, the deeper the bit goes, the wider the carving. I've successfully ...
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Using an expression and an equation to get an ODE to describe something.
I have an expression and an equation, that I need to use to show that ODE describes something.
Let me put it into context
I have an expression for the Rate at Anti-Freeze flows $\mathcal{IN}$
and $\...
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$\nu$ is a measure if $\nu(A)=\int_A f\ d\mu$ and $f:X\to [0,\infty]$ is $\mu$-measurable?
I found a result (without proof) given as an exercise in one of my measure theory texts.It says:
Proposition
Let $(X,\mathcal S,\mu)$ be a measure space and $f:X\to [0,\infty]$ be a measurable ...
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Why can't we add rates in terms of time
Why does it make sense to add some rates but not others?
Say tap $A$ takes $4$ minutes to fill a cup and tap $B$ takes $2$ minutes to fill a cup.
Then tap $A$ fills $\frac 1 4$ of a cup in a minute ...
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Estimation of $\lambda$, $\mu$, and $\sigma^2$ given observations of $Z=X+Y$, $X\sim\text{Poi}(\lambda)$, $Y\sim\mathcal N(\mu,\sigma^2)$
Let $X\sim\operatorname{Poisson}(\lambda)$ and $Y\sim\mathcal N(\mu,\sigma^2)$ be independent and define $Z=X+Y$. The density of $Z$ can be described as an infinite Gaussian mixture of the form
$$
f_Z(...
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Real life applications of severable complex variables functions theory and complex geometry
I'm studying several complex variables functions and complex geometry this semester, I knows that complex analysis has applications in electrodynamics and fluid mechanics, and differential geometry ...
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Name of the functional $p \mapsto P_X[p] = X\int_X^\infty p(x)\,dx$
Let $p(x): \mathbb{R} \rightarrow \mathbb{R}^+_0$ be a probability distribution with $\int_{-\infty}^\infty p(x)\,dx = 1$. Is there a special name for the parametrized functional
$$p \mapsto P_X[p] = ...
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What are some applications of the Fano plane and other finite project planes?
For context, I'm an undergrad studying math. In one of my courses, my professor taught us about finite projective planes and, in particular, the Fano plane. I've skimmed the Wikipedia page and read ...
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How to Calculate Antilogarithms Without Using the Log/Anti-Log Table? [duplicate]
In Logarithms and Antilogarithms,calculation of Logarithms seems easy after knowing the properties,calculation of Antilogs seems entirely difficult without using the Log-Antilog Table.I've tried ...
user1022112
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What are some interesting real-world applications of metrics?
I'm looking for ideas of real-world applications of different types of metrics/distances — especially (but not only) taxicab and railway metrics. By "real-world" I mean something that ...
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Which equations can be solved by Boost C++ library’s ibeta_inva, ibeta_invb, and gamma_q_inva functions?
All functions in this question are directly from this Boost C++ library page. These functions find the value of a random variable such that the distribution of the random variable equals a given ...
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Solver for simple probability evaluation
I'm looking into a simple probabilistic evaluation that goes like this:
Given an unknown probability $p$, $0 < p < 1$, which is assumed to have the same value for each event, a known count $n+1$ ...
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On which 2D surfaces in 3D can a Kagome lattice pattern be drawn using three sets of parallel lines"?
In the background/introduction to my Space SE question Have Kagome lattice patterns been used as structural reinforcement in spacecraft in non-Iranian spacecraft? Can we help Scott Manley "unsee&...
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Using integration to find the population $x$ after a time $t$ years. Having a problem with getting a negative log input.
I'm a little bit confused by a question I came across. It says:
If there were no emigration the population $x$ of a county would increase at a rate of $2.5 \%$ per annum.
By emigration a county loses ...
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Question in population dynamics using exponential growth rate equation
Given population doubles in 20 minutes, what is intrinsic growth rate r?
Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N(t)=N_0e^{2t}$ therefore r=2, ...
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Does this function come up anywhere in mathematics? $f(s)=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\zeta(-ns)$
I'm wondering if anyone knows if this function comes up anywhere in mathematics:
$$f(s)=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\zeta(-ns)$$
where $\zeta(s)$ is the Riemann Zeta function.
I'm asking because ...
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Geometric example of quasi-abelian category (not abelian)
Good morning to everyone,
I am writing here because I need to understand better some topics about quasi-abelian homological algebra.
Is there an example of quasi-abelian category and non abelian, in ...
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Determining correlations of derivatives of a function given only measurements of that function
Cross-posted from statistics stackexchange:
Say we have a permanent-magnet DC motor that roughly obeys the system equation $\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma$, where $x(t)$ is the ...
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Applications of unbounded measures outside of mathematics [closed]
Revised based on comments.
Measure-theoretic probability is used in finance (among other fields).
However, was wondering where unbounded measures are used, outside of mathematics and physics. For ...
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Is one SAT guessing strategy better than another?
The context is this paragraph from my SAT & ACT Prep book on page 11.
"There is one thing to keep in mind: Pick one letter for the SAT or a two-letter combo for the ACT and stick to it ...
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What are the applications of Complex numbers in Control theory?
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behaviour of dynamical systems with inputs, and how their behaviour is modified by feedback.
What I am ...
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$H^2$-regularity in space for linear parabolic equation
Consider the second order linear parabolic PDE:
\begin{eqnarray*}
\partial_{t}u + Lu &= f && \text{ in $\Omega \times (0,T]$},\\
u &= 0 && \text{ on $\partial \Omega \times [...
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Why does the sign in Newton's method matter?
Deriving Newtons Method visually as with the help of a right triangle and assuming $x_1$ lies the left of $x_0$ we get $$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)}$$
Using slope over run.
but if we assume $...
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A smooth $Q \in \mathbb R^N \to \mathbb R$ close to, but strictly below min
So, I've noticed that in many realworld applications, strict bounds are a requirement. I'll use a factory with $N$ inputs as an example. Suppose the inputs are organised into lots, and one output ...
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An application based word problem on linear equations
A thief escaped from police custody. Since he was sprinter he could clock 40 m/hr. The police realized it after 3 hr and started chasing him in the same direction at 50 m/hr. The police had a dog ...
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Simultaneous equating of partial derivative expressions
Algebraic geometers study the simultaneous vanishing of systems of multivariate polynomials.
I was wondering if this theme presents itself in partial differential equations and analysis. What I had in ...
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Hilbert's Hotel's plates, apeirotypography, and diminishing returns
Hilbert's Hotel's Plates, apeirotypography, and diminishing returns
1. What?
So I was browsing for videos about some mathematics (as one does), and I stumbled across a comment wondering how the ...
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What are the applications of dynamical odometers?
Let $\mathbf{s} = (s_0, s_1, s_2, \ldots), s_i > 2$, be a sequence and let $\Delta_{\mathbf{s}}$ be the set of all sequences of nonnegative integers $\mathbf{a} = (a_0, a_1, a_2, \ldots)$ such that ...
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Seemingly conflicting notions of a function
Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is:
A function is a a type of mathematical object that maps every element of a ...
user997478
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Which are good books for applications of Shannon Information Theory?
I am a math student, and I'm doing my final graduation project on the Shannon's Information Theory for Continuous Gaussian Channels (Differential Entropy, Time Discrete and Time Continuous Gaussian ...
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How to solve simple differential equation (biology)
First of all, I am a biologist and I am not really knowledgeable in mathematics. Thus, I apologize if what I am asking is naive or not fully explained.
I am trying to solve analytically a differential ...
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What is the advantage of using Gradian to measure an angle?
What is the advantage of Gradian to measure an angle? For example, I know radian is useful in Calculus because e.g. it simplifies the derivative of trigonometric functions.
By the way, except the ...
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Where are Sums of series of complex numbers used in real world?
While studying complex numbers, I came across topics like:
Sums of series of complex numbers
Nth roots of complex numbers
and so on...
However, I haven't actually found any 'real life' uses of them. ...
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Most efficient method to selectively wrap, with 98 percent accuracy, 10 million marbles using an imperfect machine and imperfect humans.
First just a note that this isn't a textbook problem but rather a practical problem I'm trying to solve in the real world (not involving marbles, but the problem is essentially the same). That's why ...
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Doubt on proving a given application is symmetric.
Exercise. Prove that a certain application, with $d(x,x) = 0$ is a pseudo-metric iff $d(x,z) \leq d(x,y)+d(z,y).$
What I've done so far. I have been able to prove the $(\Rightarrow)$ implication and ...
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How is the actual value of curvature applied/what can be inferred about the amount of curvature?
Let $\gamma$ be a smooth regular plane curve. We know that the curvature of $\gamma$ at $t$ is given by $||\gamma''(t)|| = \sqrt{x''(t)^2 + y''(t)^2}$, and the radius of the curvature at $t$ is $R(t) =...
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Thomas Calculus wrong question on Differential Equation?
The problem:
An antibiotic is administered intravenously into the bloodstream at a constant rate $r$. As the drug flows through the patient's system and acts on the infection that is present, it is ...
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I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
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Applications of Model Theory and Category Theory
Do Model Theory and Category Theory have applications in solving Complexity and Game Theory problems in computer science?
I am looking for an example of these...(If there is any...)
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Work on a chain (applications of the integral)
A 10-foot-long chain weighs 25 lbs. And hangs from a ceiling. Calculate the work done in raising the lower end of the chain to the ceiling so that it is at the same level as the upper end.
Please, ...
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Calculus applications - oil leaking from a boat
So here is the question:
The fuel from a ship leaks into the sea forming a circular oil slick. The area of this circle is increasing at the rate of $20$ $m^2$ per minute.
They asked me to prove that ...
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Are limits as incredibly cool as I think they are?
I recently did all the limit maths, but I didn't put much thought into its significance. I thought, okay, it's perfectly reasonable to say that, for example, as $x\to 1$, $(\frac{x^2-1}{x-1})\to2$. ...
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Using 3D Piecewise Functions to Model a Rollercoaster
I am designing a roller coaster using functions (ie. linear, cubic, logarithmic, trigonometric). At some point, one of the parts of the rollercoaster does not follow a two dimensional graph, but ...
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Whenever we get undefined or indeterminate expressions in the real world, do we just take the limit, if it exists?
In the real world, that is, in engineering, computer science, or whatever, whenever we get undefined or indeterminate expressions, do we just take the limit, if it exists? Does this work in the real ...
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Strong solutions of SDEs in electrical engineering
I am currently reading about existence and uniqueness theory for stochastic differential equations (SDE). Two of the main concepts are: strong and weak solutions.
I do understand the difference ...
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Lifetime with exponential and Poisson distribution
The lifetime of an electronic device is a rv with exponential distribution ($\mu=1/10$). In a normal week, the hours that the device is used is a rv with Poisson distribution ($\lambda=12$). Calculate ...
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Applications of matrix differentiation
I know that ordinary differentiation has many real world applications, from quantum physics to economics, but I cannot think of any real world applications of matrix differentiation. So, do any real ...
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