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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1answer
41 views

Mixture of mixtures.

I am formulating this problem for work, so it is important that I get it right. As of right now I am only considering the case where the number of chemicals is equal to the number of pre-made ...
0
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1answer
46 views

Mixing chemicals in ratios

I am trying to figure out a mixing problem and I'm stuck because it seems to have two levels. I'm going to write a simpler form here of the problem I am working on. Say that we have 60 pounds of a ...
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0answers
29 views

How to choose assymetry for KL divergence?

I have two 2D probability distributions of eye movements of two different images. Suppose I call the first distribution of Image 1: $P$, and the second distribution of image 2: $Q$. Since KL-...
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0answers
64 views

Math-a-magic: How to force all participants onto same color squares of checker board?

Setup Setup 3x3 checker board. X O X O X O X O X Rules Audience picks a random square on the board for their point of origin. [not sure if this ...
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2answers
168 views

Calculus - Finding the Linear Equation which equals area

I am really stuck on this question... I think it involves finding integration but am struggling to understand the concepts involved. I have attempted the equation $y=70$ through trial and error, ...
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0answers
51 views

Examples and applications of homogeneus models in model theory.

Does anyone know any specific examples or applications of homogeneus models, to model theory or any other branch? For example, an application would be that prime models are isomorphic in a countable ...
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0answers
19 views

Fourier coefficients for pattern analysis

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
1
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2answers
116 views

Need a textbook for math course

The undergrad course is called intro the applied math, and it covers: "The unit introduces some of the principal mathematical techniques such as difference equations, differential equations and ...
0
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1answer
49 views

Equilibrium and Stability of Nonlinear Interactions

Examine the nonlinear model: $$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$ $$\triangle y_t = -dy_t+\epsilon x_ty_t$$ Find the equilibrium and their stability. Here all the parameters are ...
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0answers
148 views

Real Mathematics in Video Games

Out of curiousity (and perhaps also to amuse my students), I am looking for examples of actual mathematics appearing in video (computer) games. Of course that sort of mathematics would probably be ...
0
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1answer
110 views

Solving Eikonal Equation

The problem is the following: I have the bidimensional eikonal equation with non-constant propagation: $u_x^2+u_y^2=u^2$ The goal is: i) To find the characteristic strips for the parametrization $...
3
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2answers
75 views

How can Bayesian and Frequentist approach be different?

Let's say I am trying to add numbers, like say one to ten. I can either add them in order, or I can notice that I can group them into five groups of eleven, so I suppose which method to use depends on ...
2
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2answers
214 views

Interesting calculus problems for beginner

Recently I started learning calculus and I think I have grasped the basics. However when calculating examples I tend to drift away and not put much effort in it. When I was learning programming in ...
2
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0answers
175 views

Moment of inertia : How to find out perpendicular distance?

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis of length ...
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1answer
109 views

System of equations and the Brouwer's Fixed-Point Theorem.

Let's consider the following system of equations: \begin{eqnarray}{ e^{xyz} = \frac{x}{\sqrt{e^{2xyz}+1}}\\ \cos(x+y+z) = \frac{y}{\sqrt{e^{2xyz}+1}}\\ \sin(x+y+z) = \frac{z}{\sqrt{e^{2xyz}+1}} }...
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6answers
749 views

Honest application of category theory

I believe that category theory is one of the most fundamental theories of mathematics, and is becoming a fundamental theory for other sciences as well. It allows us to understand many concepts on a ...
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2answers
499 views

What are some real life applications of least squares problem?

I'm looking for some applications that require solving the least square problem. I know polynomial fitting is one of them, but sure there are many others. Thanks
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0answers
52 views

Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)

Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
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0answers
63 views

Kahler-Einstein Metrics in Physics - Topic Suggestions

I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the ...
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0answers
41 views

partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from yt(...
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0answers
112 views

Why are noetherian and artinian modules important?

As a TA I was recently asked to give the students an introduction to two (quite related) concepts that are new to me, noetherian and artinian modules. I intend to prove the characterisation theorem (i....
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0answers
18 views

Determine the multi-dimensional relationship given the data

I have a dependent variable - A and 3 independent variables, H,V and N I have a data for all the variables and dependency relationship is based on my operational knowledge. I'd like to know what ...
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1answer
73 views

application of kinematics and the rates of change

A ladder 20 feet long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 3ft/sec, how fast is the ladder sliding down the building ...
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2answers
743 views

Finding the rate of rising water. [duplicate]

Water is pouring into a conical tank at a rate of 8 cubic feet per minute. If the height of the tank is 12ft, and the radius of its circular opening is 6ft, how fast is the water level rising when ...
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2answers
118 views

Show that the cubic equation has one real roots

Show that $x^3+ax+b=0$ has a) only one real root when $a>0$ b) at most only one of it's roots are in $(-\sqrt{-a/3},\sqrt{-a/3})$ when $a<0$. For a) I supposed that it had two real roots ...
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1answer
222 views

book to learn calculus by examples and real world applications

Don't know if it's the right question in this section I'll ask it anyway. When I study math I barely understand theorems, but after being given the examples I can understand the theory behind it. The ...
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1answer
65 views

The wave equation with forcing function

What would the solution to this problem be? $\frac{1}{x} u _t - (x u_x )_x = \frac{1}{x} \ln{x} \quad 1<x<e \quad t>0 $ $u(x,0) = \sin{(\frac{\pi}{2}\ln{x})} \quad (1<x<e) $ $u(1,t)=...
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0answers
51 views

Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
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2answers
338 views

Determining how long a body has been dead using the number e

I have recently seen a quote about determining how long a body has been dead: “Dead bodies lose heat exponentially, and therefore e can be used in an appropriate equation to determine how long ...
3
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1answer
269 views

Mathematical Formulas for Game Battle Calculations

I am from a programming background and trying to write a game for fun. I am trying to write a battle calculator and which ever way I think about it I seem to run into trouble. Basically the scenario ...
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0answers
49 views

What problems are related with the following type of FDE with delay?

Consider the following class of functional differential equations with delay: $$\begin{align} \frac{du}{dt} &= F(x,t,u(x,t),u_{t,x}), & (x,t) &\in [a,b] \times [0,T] \\ u(x,t) &= \psi(...
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4answers
165 views

How does Volume work with integration?

Using a cross section suppose, as described here: Area formula Paul Notes Suppose this is: $y = f(x)$. He says the volume is: $$\int_{a}^{b} A(x) dx$$ But how does area over that interval ...
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1answer
89 views

Mixed Integer Linear Programming: Construction Rods

I have an interesting problem involving linear programming. The problem is the following, I have 4 different kinds of rods (rod sized found in the local market): 9m rod 11m rod 12m rod 15m rod ...
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1answer
22 views

Volume of Revolution $f(x) = x^2$

Suppose you are given $y = f(x)$ I want to use double integrals, instead of the traditional washers. Suppose even better, $f(x) = x^2$ Find the volume of $f(x) = x^2$, $x = 0$, $x = 4$, $y = 0$ &...
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1answer
72 views

How is it possible to change the pitch and the tempo of an audio track independently of each other?

If you slow down a turntable or cassette-player, both pitch and tempo are decreased. How is it possible to change one without affecting the other?
2
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0answers
81 views

Sturm-Liouville problem with vibrations - probably easy for most.

Trying to do this one... A model for the transverse vibrations of a stretched string with variable density ρ and tension τ (both continuous and strictly positive on the closed interval [0,l]): PDE: $...
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1answer
75 views

Graph theory application of homology

I am struggling with the idea of local homology groups and would like to see an example of how to go about finding them in general. I'm thinking of the most trivial case to apply the theory of local ...
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0answers
165 views

Rotational matrix problem?

In the problem yo-yo is made of two identical cylinders of radius $R$, thickness $h$ and mass $M$, and the yo-yo is let go. In order to define the position of the yo-yo, I need as position vector and ...
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1answer
261 views

Center of mass of a trick sphere-cone intersection

B is the solid region occupying the space situated inside the sphere of radius R centered at the origin and above the cone of equation $z = \sqrt{x^2 + y^2}$. The B density is proportional to the ...
2
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1answer
42 views

Uniform acceleration

Two stunt drivers drive their cars along a straight horizontal road. The first car is travelling at 30 m/s and is followed by the second car, 16 m behind it, both cars are travelling with equal speeds....
0
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1answer
50 views

Uniform acceleration (easy question)

Two stunt drivers drive their cars along a straight horizontal road. The first car is travelling at $30$ m/s and is followed by the second car, $16$ m behind it, both cars are travelling with equal ...
2
votes
1answer
169 views

applications of linear differential equations

I’m writing a paper on the applications of linear differential equations[undergraduate level] could be in physics, chemistry, engineering, business..etc, since I am fairly new to doing research, can ...
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2answers
49 views

Objects falling.

A small ball is released from rest and falls on a horizontal platform which is descending vertically at a constant speed of 7m/s, If the ball is 14 m above the platform at the instant of release, ...
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2answers
122 views

Relation between distance s and velocity v is given by $v=\dfrac {150s} {3+s}$

I am stuck on this related rates question: The relation between distance $s$ and velocity $v$ is given by $v=\dfrac {150s} {3+s}$. Find the acceleration in terms of s. So far I have: $$\dfrac {dv} {...
0
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1answer
743 views

Solve for the charge on a discharging capacitor in an RC circuit using Laplace Transforms. (5.3-61)

Please check my work. I need to solve the following problem but my answer varies from that of the book by a factor of $C$ for capacitance. A print screen of the problem is given below. Problem to ...
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0answers
24 views

House allocation with existing tenants

In a house allocation with existing tenants model using the TTC mechanism, consider the incentive of an agent to misreport his/her preferences. Can it ever be that misreporting the true preferences by ...
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0answers
45 views

Time taken to empty a hemispherical shaped tank

The tank has a radius of $2$m when initially filled and has an outlet of cross section $12$ cm2 Outlet flow as I calculated goes according to the law $V(t)=0.6\sqrt{2gh(t)}$. Having found out the ...
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1answer
228 views

Rate of change question involving velocity, displacement and acceleration

I have been having trouble understanding questions c)-e) and am in need of some help: An object is moving in a straight line from a fixed point. The displacement $s$ in metres is given by $s=-2t^2+...
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17answers
8k views

Is the Law of Large Numbers empirically proven?

Does this reflect the real world and what is the empirical evidence behind this? Layman here so please avoid abstract math in your response. The Law of Large Numbers states that the average of the ...
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2answers
107 views

Finding maximum of convex function (appliance of derivatives)

The task goes as following: Divide the length of $14$ into parts $a$ and $b$, in a way that the sum of surfaces of two squares (which sizes are $a$ and $b$), is minimal. $14=a+b => b=14-a$ $....(...