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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Mathematical statistics: Pollen dispersal directionality

What Information am I looking for? Think about a tree that is sending pollen all over the place. Because of wind, most pollen grain will go toward one direction. Imagine, we split the 2D area around ...
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Hydrostatic Force on a submerged plane.

I am having trouble with question 5, it reads (ignore the Riemann sum part) : Here is what I did, and where did I go wrong?. The answer the book gives is: $6.7\cdot 10^4N$. Thank you.
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How to practically make use of Mathematics? [closed]

How to practically make use of Mathematics ? I have a basic question.How to use Mathematics in our modern day lives? Are there any ways by which we can make Mathematics come out of our classrooms and ...
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51 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 ...
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1answer
49 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 ...
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2answers
63 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 ...
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2answers
66 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 ...
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0answers
49 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
52 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
526 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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14 views

Application of Riesz Spaces (k/a $K$-Lineals or Vector Lattices ) to Mathematical-Economics?

From Wikipedia: "C. D. Aliprantis was a Greek-American economist who introduced Banach space and Riesz space methods in economic theory." What applications are there?
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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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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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39 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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35 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 ...
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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 ...
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14 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
24 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
60 views

Finding the rate of rising water.

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
57 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
67 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
37 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) $ ...
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Name and application of a matrix encryptation method

The textbook I am using for teaching has a short section on encryptation using matrix as an application of matrix theory. The method is as follows: The persons that are allowed to encode/decode ...
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Engel Curve in Economics

I have a utility function in the form $U = B^{.67}Z^{.33}$ I am supposed to find an Engel curve assuming that the price of goods B and Z are $P_b$ and $P_z$ respectively with income level $Y$. I can ...
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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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51 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 ...
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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) &= ...
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4answers
81 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
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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
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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
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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?
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Question about uniform wire and its application to find centroid

A uniform wire has the shape of that portion of the curve of intersection of the two surfaces x^2+y^2=z^2 and y^2=x connecting the points (0.0.0) and (1.1.square root 2) Find the z-coordinate of its ...
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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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41 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
67 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 ...
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1answer
24 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 ...
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1answer
39 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 ...
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1answer
51 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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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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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} ...
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1answer
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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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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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28 views

Nash equilibrium in marriage market stable matching

Consider a marriage market where matchings are formed using the DA women-proposing algorithm. However, there is an additional constraint that only matches among agents that have previously gone out on ...
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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
34 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 ...
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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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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. $14=a+b => b=14-a$ ...
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Creating a weighted score

I have an audit where there are six criteria, each can be scored Excellent (E), Satisfactory (S), Needs improvement (N) or Unsatisfactory (U). I know that if someone scores Excellent in all six areas ...
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1answer
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How to calculate a monthly mortality rate?

If the instantaneous mortality rate for a species (or a group of humans) is 0.1/year, what is the mortality rate per month? Can you just divide $0.1/12$? This seems too simple and incorrect because ...
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Surprising applications of topology [closed]

Today in class we got to see how to use the Brouwer Fixed Point theorem for $D^2$ to prove that a $3 \times 3$ matrix $M$ with positive real entries has an eigenvector with a positive eigenvalue. The ...