# 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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### Who knows Krotov's Method in Optimal Control Theory

I'm finishing my PhD thesis about applications of optimal control theory in the field of energy harvesting. In the course of my PhD I dealt with different ways to compute optimal controls, and I found ...
5answers
52k views

### How does linear algebra help with computer science?

I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult ...
0answers
90 views

### how to compute the intersection of two hyperbola branches

I am trying to develop an idea to determine the location of a cell phone using OTDOA (obseved time differences of arrival). The base stations emit electromagnetic wave to the cell phone, the cell ...
1answer
38 views

### How do GPS receivers keep accurate on-board time? [closed]

GPS, or Global Positioning System is a network of satellites in orbit above the surface of the Earth. By the satellites constantly transmitting their exact position and on-board time through radio ...
0answers
526 views

### Importance of graph planarity for applications

What is the real-life motivation for studying (or inventing) effective algorithms to check whether or not a graph is planar (which seems to have garnered interest in recent years)? Why is planarity an ...
2answers
433 views

### What algorithm do scientific calculators use to calculate Logarithms

I have been introduced to numerical analysis and have been researching quite a bit on its applications recently. One specific application would be the scientific calculator. From the information ...
1answer
199 views

### Motivation for the Basel problem

I realized that I know of several ways how to prove that $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$, but I have no idea why I would want to know the answer in the first place. Answers I have ...
0answers
80 views

### Learn Calculus with applications instead of rigor

OBJECTIVE: I am looking for some resources/books to learn Calculus. I have searched archives here and noticed that recommended books from reputed authors Spivak, Courant, Hardy, Apostol are based on ...
9answers
13k views

### Real world applications of category theory

I was reading some basic information from Wiki about category theory and honestly speaking I have a very weak knowledge about it. As it sounds interesting, I will go into the theory to learn more if ...
7answers
7k views

### What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
2answers
1k views

### Curve on a basketball

The sewing pattern on a basketball is composed of two great circles and a single curve that intersects each great circle twice. Does this curve have a name? Are there any parametric descriptions of ...
1answer
165 views

### Modeling Real World Situations / Trigonometric Functions

I got this question and it seemed to be tricky! You are standing at a base of a Ferris Wheel which is 4 m above ground while your friend is riding. The Ferris Wheel is 8m in diameter. Describe how ...
4answers
255 views

### How to explain to kid why subtraction is not commutative

My 7-year old daughter (pre-school) asked why subtraction is not commutative. How to explain that in simple way, in relation to real world concepts? (I am not looking for abstract mathematical proof) ...
2answers
960 views

### Solution to ODE from Newton's Second Law

I have attempted to explore Newton's second law (F = ma) further into its many differential forms. I am not very familiar with differential equations and was searching for the steps and methods to ...
2answers
500 views

### Real world application of Lebesgue measure as opposed to Jordan measure [closed]

Are there real world applications of Lebesgue measure? I think Jordan measure is sufficient to solve real world problems.
3answers
109 views

### Finding the maximum area of a right triangle inside a right triangle

So I've encountered a question where it requires me to find the maximum area of a small right angled triangle inside a bigger one. The question stated the dimensions of the big triangle and approved ...
4answers
2k views

### What are the applications of finite calculus

I'm reading through Concrete Mathematics [Graham, Knuth, Patashnik; 2nd edition], and in the section regarding Summation, they have a sub-section entitled "Finite and Infinite Calculus". In this ...
1answer
379 views

### Your Favourite Application of the Birkhoff Ergodic Theorem

Here we have a big list of great applications of the Baire category theorem. I recently read the Birkhoff ergodic theorem and I think perhaps this theorem is on par with Baire's theorem in terms of ...
1answer
660 views

### Amount of work required for pulling rope problem

50 m rope with 8 millimeters in diameter is dangling from an edge. density of rope =40 g/m. how much work to pull it up to edge? // I've seen different variations of this problem, but I am unsure of ...
0answers
76 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}} }...
1answer
27 views

### Determining Rate of Convergence for Chaotic Behavior

I've got a set of data that's been manipulated solely numerically. But anyway, for a certain part of that data set, I see that it's convergent (image). But I'm sort of at a loss for how depict that ...
1answer
102 views

0answers
62 views

### What are some example use cases for Newton's Method being extended to higher dimensions?

I'm currently working on a project to attempt to optimize a program that runs Newton's Method in higher dimensions - the actual computer science isn't important. However, what is a lot more important ...
1answer
42 views

### Orientation of Edges in Images

I´m currently reading the paper Edge analysis and identification using the continuous shearlet transform (by K. Guo, D. Labate and W. Lim). In this paper it is written that not only the detection of ...
1answer
22 views

### A question regarding the given rates in a related rates question

I have a question about these rates given in a related rates question. For example, when it's given that the car is moving at $60\;\text{km/h}$, a balloon is heading up at $2\;\text{m/s}$, a circle's ...
9answers
26k views

### How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
2answers
259 views

### Any employment for the Varignon parallelogram?

The midpoints of the sides of an arbitrary quadrilateral form a parallelogram, which is called the Varignon parallelogram of the quad. While answering a question about Quadrilateral Interpolation it ...
2answers
881 views

### Applications of topology to logic?

At Ieke Moerdijk's homepage, one can read that his research interests include "applications of topology to mathematical logic". I know very few such applications (essentially I only know topological ...
0answers
38 views

### Probability to be overtaken on circuit

I'm running on a treadmill in the gym and use the software (provided) which basically enables me to see other people running around me in the virtual race arena (standard 400 m circuit). I'm running ...
0answers
39 views

### Color wheel in the complex plane

Is it possible to arrange the colors of the color wheel on the unit circle in the complex plane such that mixing any two colors results in the color corresponding to the product of the two ...
9answers
5k views

### Why is the derivative important? [duplicate]

Derivatives, both ordinary and partial, appear often in my mathematics courses. However, my teachers have never really given a good example of why the derivative is useful. My questions: Other than ...
1answer
219 views

### Real world applications that are modelled by Simplicial Complexes

I am interested to find out what are some real world applications that are "truly" modelled by Simplicial Complexes. Note: There are many some real world applications like social networks / neural ...
1answer
905 views

### Prime Numbers and Architecture

Prime Numbers are widely used in technology and cryptography. They are sometimes also used in small scales such as building gears and evolution of life cycle of Cicada insect. Are they in any way used ...
0answers
22 views

### Applications of differential equations that boil down to tridiagonal matrix when solved using implicit methods

I am looking for actual applications where differential equations are solved using implicit methods that boil down to solving a tridiagonal every time step. I found that there are heat equations and ...
7answers
7k views

### 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 ...
0answers
30 views

### SIR model: condition on the equation $R_\infty = 1 - e^{-\lambda k R_\infty}$ to have nonzero solution

I was reading this paper (pages 3 and 4 if you need the context), while I saw this equation on $R_\infty$ (the number of people who finally recovered): $R_\infty = 1 - e^{-\lambda k R_\infty}$. But, ...
1answer
86 views

### Multilateration of Sound in 3D Space

TL:DR - How can you find the 3D coordinates of a emitter than transmits an impulse signal? STORY: I'm working on something to improve my bird-watching. I've got a camera that can take pictures of ...
0answers
27 views

### Folding Problem

Here's one for you topologists out there to show your field has practical application. I have covers for my air conditioner units that are shaped like 5 sides of a rectangular sold with dimensions 31"...
1answer
87 views

### Why the length of the beak of birds of a certain specie follows a normal distribution. Also, IQ

A friend of mine is studying biology, and in a project of hers, she had to measure the beak (and other parts of the body) of some dozens of birds of a same specie, and analyze the data. In particular, ...
3answers
179 views

### How to find effective rate of interest?

A man charges at the rate of $10$ paise per rupee per month, payable in advance. What effective rate of interest does he charges per annum? Here rate is $10\%$ per month. So to change it in per annum,...
2answers
35 views

### Application of integrals. [closed]

What is the volume of the solid generated when the region bounded by $y=3x$ and $y=x^2 +2$ rotate about the $x$-axis ?
2answers
306 views

### Vector space without a scalar product

In linear algebra the terms vector space and scalar product always (at least for me) appear together. Can you give me an example of a vector space without a scalar product? Does the sentence Let $V$ ...
1answer
68 views

### Is it important to keep one's goal in mind when learning calculus?

I am learning calculus primarily as a prerequisite to understanding machine learning and other statistics/finance applications (Black Scholes, etc.), but I've found that most of the web content ...
17answers
13k 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 ...
12answers
13k views

### What are the applications of functional analysis?

I recently had a course on functional analysis. I was thinking of studying the mathematical applications of functional analysis. I came to know it had some applications on calculus of variations. I am ...
3answers
1k views

### Is there any result that has applications that can't be proved in constructive mathematics?

Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “ we can construct”. Is there any ...