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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Finding the work using integrals

A tank full of water has the shape obtained by revolving the curve $y = arcsin(x)$ around the y axis from $x = 0$ to $x = 1$. Find the work required to pump the water out of the tank. (The density of ...
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6answers
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Applications of Complex Numbers

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...
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1answer
76 views

Understanding a derivative in a biology article

From this biology article (5th page, right column) They have... $$1-P_t ≈ 1-(1+s)P_{t+1}+\frac{p_{t+1}^2}{2}$$ and they conclude that... $$\frac{dP}{dt} ≈ -sP + \frac{P^2}{2}$$ I don't really ...
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0answers
78 views

Using data points and a best-fit to find a function for quantity with respect to price

So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math ...
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1answer
334 views

convert circuit to nor only gates

for an assignment I need to convert a circuit to NOR gates only circuit. (A+B)C + D I know that morgan's theorem states: (a) (A+B)'=A'B' (b) (AB)'=A'+B' I've seen online how to convert some ...
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1answer
84 views

Applications of the theory of distributions outside of PDEs?

Are there any interesting, important or powerful mathematical applications to the Theory of Distributions besides those dealing with partial differential equations?
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0answers
271 views

Modeling bacterial growth with differential equations

I hope this is the right place for this question. I am working on building a growth model for bacteria for a risk assessment, and would like to move the growth model past static temperature ...
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0answers
116 views

Applications of the Kuratowski closure-complement theorem

I crossed with the Kuratowski closure-complement theorem while learning Munkres's Topology (Problem 21 in Section 17; Page 102, 2nd edition). The following description is from B.J. Gardner and M. ...
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2answers
605 views

differential area

I'm just trying to refresh my calculus a bit, I'm stuck on a question and I'd love some insight. A square measures 0.9cm on each side when drawn with a pencil. When traced over with a marker, it ...
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1answer
239 views

Find the direction of the clock arrow [closed]

A clock is placed such that at 12 noon its small arrow points towards north-east. In which direction does its large arrow point at 1.30 p.m? (A) North (B) South (C) East (D) West (E) None of these
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5answers
428 views

Why - not how - do you solve Differential Equations? [closed]

I know HOW to mechanically solve basic diff. equations. To recap, you start out with the derivative $\frac{dy}{dx}=...$ and you aim to find out y=... To do this, you separate the variables, and ...
2
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1answer
115 views

Does every major genre of mathematics have applications?

I know that it used to be said, in praise by some and as criticism by others, that Number Theory had no applications. Now it is used in cryptography and Quantum Theory. Since the mathematics that ...
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1answer
823 views

Find derivation (dB/decade) for given amplitude characteristic of low pass filter [Hz, -]

I am trying to find derivation (differential attenuation) for frequency's 600 and 2000 Hz for given amplitude characteristic of low pass filter, which look like this: I assume, that I should ...
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3answers
140 views

red and green apples

We can eat 3 apples per hour. We must eat: 3 green apples once per 2 hours. 4 red apples once per 3 hours. We can't eat fractions of an apple. The apples are named, the 3 green (A, B, C) and the ...
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1answer
5k views

Compound interest formula and continuously compounded interest formula derivation

My textbook gives the formula for compound interest as: $A\left( t\right) =P\left( 1+\dfrac {r}{n}\right) ^{nt}$ Where: P = The principal, r=the annual rate of interest, n= the frequency of ...
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3answers
156 views

Applications of functions of the form $f(x)^{g(x)}$

Early on in my calculus education, I learned how to take the derivative of $x^x$ by re-writing it in the form $e^{x\ln x}$. More generally, this technique is helpful in finding the derivative of ...
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0answers
33 views

integer programming with bounded dimension

We know that integer programming with bounded dimension or fixed number of variables can be solved in polynomial time by Lenstra's result(from results of the LLL algorithm). After heavy foraging i ...
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1answer
536 views

A real life application for QR decomposition

I need to use the QR decomposition of a matrix for a real life application, (use it on a particular matrix form) and I have no idea what to do. Can you suggest me a real life application for this? ...
3
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1answer
62 views

Topic for teaching assessment

I'm in the position to have a teaching assessment with a tutoring agency next week. This assessment will include me teaching the assessor a topic of my choice in 15 minutes, demonstrating the Socratic ...
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1answer
39 views

Calculating an exponentially increasing vector of points in a test and measure system

My application is setting and measuring current and voltage in a physical system with a software algorithm. Given these parameters: min, ...
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0answers
70 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
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0answers
91 views

Showing that pressure reaches its max on the boundary of ideal fluid in a stationary flow

The question is to show that the pressure in the stationary flow of ideal fluid achieves is maximum value on the boundary (and not at an interior point, unless the pressure is constant). I've come up ...
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2answers
113 views

Find the velocity field of ideal fluid that has a sink strength of $2\pi k$ using complex analysis.

The precise question is, find the velocity field of ideal fluid given that the fluid has a sink of strength $2\pi k$ at the origin (and no other singularities) and that it has velocity $V_\infty$ (a ...
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1answer
271 views

Background for studying and understanding Stochastic differential equations

Assume I have back ground of the following knowledge based on the textbook as : ODE : ODE by Tenenbaum Baby probability : Ross 's baby probability Baby real anlysis : Bartle's introduction to real ...
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1answer
153 views

Prove or disprove the conjecture about the function below.

After thousands of numerical tests we stated the conjecture that their is exactly one local extremum of the function below. $$ {\rm f}\left(w\right) = {1 \over 2}\sum_{i = 1}^{n}\left({1 \over 1 + ...
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2answers
213 views

What is the simplest mathematical concept that does not map to a physical phenomenon?

One of my colleagues argues that everything in math proves something in the physical world. For instance, he claims that the existence of math to describe fractals proves the infinite divisibility of ...
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0answers
170 views

How is graph theory used to solve problems in number theory?

What are some applications of graph theory in number theory? How can a graph theory approach be useful to solving number theory problems? In general, is graph theory ever useful in making number ...
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1answer
33 views

Extensions to linear control with output constraints

Does anybody know which extensions to the linear controller exist that can cope with constraints in the output value and its derivative? Usually, the plant being controlled have some limits and I ...
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0answers
27 views

basic analytical set of tools — integration, differentiation, convergence and handling of applied maths equations

I am more into mathematical logic, algebra, etc. I am asking for a scrib sheet or short and precise collection of a set of tools which somehow demonstrates the everyday set of tools for integration, ...
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1answer
340 views

Finding the “differentness” of two point clouds

I would like to reduce the "differentness" of two point clouds $X$ and $Y$ to a single comparable value $\lambda$, which would ideally be $0$ when $X$ and $Y$ are identical upto isometry (rotation, ...
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1answer
42 views

Adjust Saturation in CIE L*a*b* space.

Given a color in CIE L*a*b* space, how does one change the saturation? This is what I know... $$\mathrm{chroma} = \sqrt {(a^*)^2 + (b^*)^2}$$ $$\mathrm{hue} = \arctan \left( a^* \over b^* \right)$$ ...
11
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1answer
225 views

Applications of TQFTs beyond physics

I'm giving a talk at a postgrad seminar on the topic of topological quantum field theories (TQFTs) with a mixed audience of pure and applied mathematicians. As such, I'd like to be able to offer some ...
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1answer
188 views

Application of the weak law of large numbers (Roulette)

I am currently working on the following problem. Imagine the following situation: A player bets 1 dollar, and looses his bet with the probability of 19/37, but is given his bet and an extra dollar ...
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10answers
1k views

What are the applications of continued fractions?

What is the most motivating way to introduce continued fractions? Are there any real life applications of continued fractions?
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2answers
515 views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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1answer
48 views

Transformations problem

$$ \mbox{Let}\ x\ \mbox{have pdf}\quad {\rm f}\left(x\right) = {n \choose x}p^{x}\left(1 - p\right)^{n-x} $$ for $x = 0,1,2,\ldots,n$ where $n$ is positive integer constant and $0 < p < 1$ is ...
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1answer
239 views

What are some practical applications of mathematical/formal logic to science and humanities? [closed]

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very self facing, with logicians proving things for other logicians. It left me ...
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1answer
126 views

Planning a mockup maths class for high school related to river reactivation

I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for ...
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4answers
2k views

“Real”-life applications of algebraic geometry

Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. I did my undergraduate degree in mathematics, ...
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0answers
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vector calculus work done line integral

A string lies along the circle $x^2 + y^2 = 4$ from $(2,0)$ to $(0,2)$ in the first quadrant. The density of the string is $ρ(x,y) = xy$. a. Partition the string into a finite number of sub-arcs to ...
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1answer
62 views

How do I model a real life observation with mathematical expression or equation(s)?

I am looking for a guide to learn how to model real life situations into mathematical equations and able to simulate them. My target is to able to understand and interpret something I observe into a ...
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0answers
95 views

Applications of Numerical methods

I'm in a course of Numerical Methods and part of an assignment is find an article about an application of numerical methods, explain this article and present a program (in matlab/octave) that ...
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1answer
82 views

Motivation and application for stochastic geometry.

I am starting a PhD, and there is a good chance that my project will be oriented in the study of random polytopes or/and random mosaics. I was wondering what are the motivations and applications of ...
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2answers
6k views

What are the applications of matrices in real world?

Matrices are considered very important in mathematics. What are some examples of applications of matrices to real world problems that would be understandable by a layman?
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1answer
23 views

Evaluate a Variable Defined in Terms of its Function

I have a variable x which is defined as follows: x = 150 / (7 + f(x)) where f(x) = 0.005 * x if x > 200, or 100 otherwise. This is actually a simplified version of a real world problem. How do I ...
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1answer
25 views

Continuity- Image of a function

I have the following topological space: $\tau=$ {$U\subseteq R: 1\notin U$} U {$R$} and the following application: $f: (R, \tau)\to (R, \tau)$ I have to see that if f(1)=1, then f is continuous. ...
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3answers
56 views

Role of differentiation in a polynomial

I have learnt that, to find maximum or minimum value of a polynomial $p(x)$, we take its derivative, equate it to zero, solve for x, find the maxima and minima, and then put the value of x in the ...
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1answer
112 views

Area under the curve

suppose we have graph of $\sin(x)$ and a ellipse say $\frac{x^2}{10}+\frac{y^2}{2}=1$ it comes like following now when we intregrate $\int_{0}^{2\pi}\sin(x)dx$ it comes out to be zero , because ...
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5answers
292 views

How can I express the sum of $\sin a+\sin2a+\sin3a+\cdots+\sin(n-1)a$?

I want to sum up the partials of a harmonic series, how do I do it? If I was using the 'Lagrange trigonometric identity to solve this problem', how would I plot it on Wolfram mathematica (using which ...
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1answer
922 views

Optimisation of a rectangles area under a function curve

I have a questions asking for the dimensions of the rectangle with the largest area that has two bottom corners on the x axis and two top corners on the curve $y=12-x^2$. I have plotted the curve and ...