# 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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### Applications of mathematics in studying red pandas? [closed]

I'm currently an undergrad in mathematics and love red pandas. How can higher-level mathematics be applied to researching red pandas? I don't have a specific type of research in mind, simply because I'...
1 vote
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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 ...
44 views

### 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 ...
43 views

### Simplicial complex [closed]

I started to learn about "simplicial complex" and read about applications but it was very difficult for me to understand these applications, my question is as below what is the importance ...
17 views

### Applications of Diophantine equations? [duplicate]

It had proved that there is no algorithm to solve Diophantine equations, for that reason I want to know what are the Diophantine equations that physicists or chemists need to solve? or any other ...
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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 $... 0 votes 0 answers 21 views ### What are partial differential equations with fast reaction terms? I know$u_t(t,x)=\Delta u^m(t,x),\;\; (t,x)\in (0,\infty)\times \mathbb{R}$is the fast-diffusion equation when$m\in (0,1).$But how are PDEs with fast reaction terms defined in general? I also wish ... 1 vote 1 answer 15 views ### A smooth$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$inputs as an example. Suppose the inputs are organised into lots, and one output ... -1 votes 1 answer 35 views ### An application based word problem on linear equations A thief escaped from police custody. Since he was sprinter he could clock 40 m/hr. The police realized it after 3 hr and started chasing him in the same direction at 50 m/hr. The police had a dog ... 1 vote 0 answers 29 views ### Simultaneous equating of partial derivative expressions Algebraic geometers study the simultaneous vanishing of systems of multivariate polynomials. I was wondering if this theme presents itself in partial differential equations and analysis. What I had in ... 1 vote 0 answers 35 views ### Hilbert's Hotel's plates, apeirotypography, and diminishing returns Hilbert's Hotel's Plates, apeirotypography, and diminishing returns 1. What? So I was browsing for videos about some mathematics (as one does), and I stumbled across a comment wondering how the ... 3 votes 0 answers 44 views ### What are the applications of dynamical odometers? Let$\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)$such that ... 3 votes 1 answer 53 views ### Seemingly conflicting notions of a function Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is: A function is a a type of mathematical object that maps every element of a ... 1 vote 1 answer 63 views ### Which are good books for applications of Shannon Information Theory? I am a math student, and I'm doing my final graduation project on the Shannon's Information Theory for Continuous Gaussian Channels (Differential Entropy, Time Discrete and Time Continuous Gaussian ... 0 votes 1 answer 86 views ### How to solve simple differential equation (biology) First of all, I am a biologist and I am not really knowledgeable in mathematics. Thus, I apologize if what I am asking is naive or not fully explained. I am trying to solve analytically a differential ... 0 votes 1 answer 53 views ### What is the advantage of using Gradian to measure an angle? What is the advantage of Gradian to measure an angle? For example, I know radian is useful in Calculus because e.g. it simplifies the derivative of trigonometric functions. By the way, except the ... 0 votes 1 answer 39 views ### Where are Sums of series of complex numbers used in real world? While studying complex numbers, I came across topics like: Sums of series of complex numbers Nth roots of complex numbers and so on... However, I haven't actually found any 'real life' uses of them. ... 1 vote 0 answers 35 views ### Most efficient method to selectively wrap, with 98 percent accuracy, 10 million marbles using an imperfect machine and imperfect humans. First just a note that this isn't a textbook problem but rather a practical problem I'm trying to solve in the real world (not involving marbles, but the problem is essentially the same). That's why ... 1 vote 1 answer 26 views ### Doubt on proving a given application is symmetric. Exercise. Prove that a certain application, with$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)$implication and ... 0 votes 0 answers 21 views ### How is the actual value of curvature applied/what can be inferred about the amount of curvature? Let$\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) =...
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 ...