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.)

learn more… | top users | synonyms

0
votes
1answer
63 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
0
votes
1answer
30 views

Matrices in Linear Algebra

Let: $ u: R^2 --> R^3$ be defined by: $$ u(x,y)=(x+2y, 2x-y, 2x+ 3y)$$ Give the matrix $M[u]$ in the canonical base of its definition space. This question might seem sort of stupid, but it was ...
0
votes
2answers
829 views

Practical use and applications of improper integrals

What are the most important applications of improper integrals, in particular to computer science and related fields, and to technology and engineering in general? I know that improper integrals are ...
2
votes
0answers
290 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
1
vote
2answers
65 views

Function application (word problem)

The problem: My work so far: $3=log(\frac{A}{A_0})$--->$10^3=\frac{A}{A_0}$ $\frac{A}{A_0}=1000$ (Am I done there?) Plugging it in: $M=log(\frac{1900000}{1000})$ $10^M = \frac{1900000}{1000}$ ...
1
vote
1answer
35 views

How to write this function?

I do not want the answer given to me, I just want assistance. Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account ...
3
votes
1answer
162 views

Applications of simultaneous diagonalization of quadratic forms

If $A$ and $B$ are square symmetric matrices and, additionally, one of them, say $B$, is positively defined, then there exists an invertible matrix $S$ such that $$S^{\top}\!AS=D ...
3
votes
3answers
891 views

Maximum possible variance

From this biology article, end of page 4, the author talks about a random variable which never takes value outside the range [0,1] (0 and 1 included in the range). He says that the maximum variance ...
0
votes
1answer
33 views

Amount of Liquid in Container

Given: a cuboid container, of dimensions h into w into l a rate of flow of liquid per unit time through an inlet, in a rate of flow of liquid per unit time from an outlet, out, when the container ...
1
vote
0answers
38 views

Nyquist diagram of transfer function

Transfer function of a system is given as $$G(s) = \frac{100(s+5)}{s^2(s+3)(s^2+4)}$$ Sketch the Nyquist diagram and find if the system is stable. Also find the gain margin and phase margin. Please ...
2
votes
2answers
345 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 ...
1
vote
1answer
307 views

Calculus - Trig Maximum Value Problem

When the rules of hockey were developed, Canada did not use the metric system. Thus, the distance between the goal posts was designated to be six feet. If Sidney Crosby is on the goal line, three feet ...
0
votes
2answers
2k views

Real world tangent functions

I am a high school math teacher and one of my students asked me for examples of real world tangent functions. Not using tangent to find a side length but a relationship that can be represented by a ...
0
votes
1answer
109 views

Application of derivatives: related rates problem

Water is leaking out of an inverted conical tank at a rate of 50L/min the tank is 10m in diameter at the top. It is 6m deep at the deepest point, which is the vertex of the cone and lies on the ...
2
votes
0answers
65 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
4
votes
4answers
428 views

What is Cramer's rule used for?

I could have sworn I posted the question in the subject line somewhere on the internet, and I thought it was here. But I can't find it. It ought to be here in case anyone looks for it. Cramer's ...
3
votes
1answer
141 views

Volume vs. Surface Area Integrals

In order to find the volume of a sphere radiud $R$, one way is to slice it up into a stack of thin, concentric disks, perpendicular to the $z$-axis. a disk at any point $z$ will have radius ...
1
vote
1answer
241 views

The golden ratio in statistics of literature

Let a book, for example, or a poem... It consists in words and letters and symbols like : ;,!... Let $W_b$=the number of words of the book. Let $L_b$=the number of letters of the book. The number ...
0
votes
3answers
586 views

Britney Gallivan's paper folding formulas

According to a few YouTube videos and New Scientist, formulas exist (based on algebraic/mathematical premises, thereby making this a valid math question) to describe the limits of paper folding. The ...
1
vote
1answer
38 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
0
votes
0answers
436 views

Volume enclosed by two spheres (triple integral, cylindrical coordinates)

The question: Find the volume of the solid enclosed by the sphere $x^2 + y^2 + z^2 - 6z = 0$ , and the hemisphere $x^2 + y^2 + z^2 = 49 , z ≥ 0$ I set up the triple integral ...
28
votes
2answers
410 views

Statistics Primer for the Unwary Mathematician

I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical ...
3
votes
3answers
1k views

Real world situation with System of Equation with 3 variables?

Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
1
vote
1answer
118 views

Probability distribution of the product of random numbers

For applied mathematics to evolutionary biology I am often faced to have to describe a probability distribution function (PDF) which results from the product of a function in which a parameter is ...
11
votes
2answers
803 views

Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...
1
vote
1answer
218 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
0
votes
6answers
7k views

Application of Composition of Functions: Real world examples?

Do you know of a real world example where you'd combine two functions into a composite function? I see this topic in Algebra 2 textbooks, but rarely see actual applications of it. It's usually plug ...
7
votes
4answers
283 views

An unexpected application of non-trivial combinatorics

PROBLEM STATEMENT Given two finite sets $A$ and $B$, each containing $s \in \mathbb N$ elements, how many pairs of functions $f \colon A \rightarrow B$ and $g \colon B \rightarrow A$ are there, ...
2
votes
1answer
1k views

Real world applications of exponential function; continous case

I am looking for interesting applications in everyday life, technology or science of exponential functions of the type: $$ f\colon \mathbb{R} \to \mathbb{R}, \quad x \mapsto ab^x $$ for the case $a ...
2
votes
2answers
42 views

Application of the spectrum of an operator

http://en.wikipedia.org/wiki/Spectrum_of_an_operator What is the application of the spectrum of an operator
0
votes
2answers
1k views

How to find (and plot) a probability distribution function?

I'm working on my biometrics course, and I have to plot a pdf (I think it means probability density / distribution function). Here is a sample pdf graph : Introduction to Biometrics page 5 , figure ...
3
votes
0answers
44 views

Mathematical analysis of e-shop

I'm ukrainian student, studying applied mathematics in Kiev. I have an online store and some statistics data on it's work. Also I've learned a bit about optimization problems and operation reasearch. ...
5
votes
2answers
1k views

Applications of Perfect Numbers

I'm preparing a talk on Mersenne primes, Perfect numbers and Fermat primes. In trying to provide motivation for it all I'd like to provide an application of these things. I came up with these: ...
1
vote
2answers
238 views

A model for the spruce budworm population

A model for the spruce budworm population $u(t)$ is governed by $$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$ where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
5
votes
4answers
417 views

Why use differentials to compute error?

I get how to use differentials to compute error, but why is it a "good" method? For example, a standard problem is something like: If the radius of a circle is $3 \pm 0.1$ cm, find the area with ...
2
votes
1answer
221 views

Would a risk averse agent ever accept gambles with negative expected value? [closed]

Consider a risk-averse agent (his utility for money is strictly concave) that maximizes expected utility. Would such agent ever a accept a gamble whose expected value is negative? (e.g. think of state ...
4
votes
1answer
104 views

Who generates the prime numbers for encryption?

I was talking to a friend of mine yesterday about encryption. I was explaining RSA and how prime numbers are used - the product $N = pq$ is known to the public and used to encrypt, but to decrypt you ...
-1
votes
2answers
214 views

What are the applications of algebraic geometry to electronics?

I am currently pursuing an undergraduate degree in Electronics and Communications Engineering in India. I recently got a research internship to study algebraic geometry for two months at a highly ...
5
votes
3answers
132 views

On trusting the mathematical process [closed]

In studying math we are, at least partially, interested in making abstraction of real world problems and solving them through rigorous techniques and methods, and then interpreting the result. Let us ...
1
vote
1answer
37 views

Get pair number of given shelf number

I work at a warehouse, and have shelves organized in that way: ...
0
votes
1answer
48 views

please help me understand the lecture note? heat equation and fourier series

I don't quite understand equation 3.73 and 3.74. To get $T(x,t)$ I thought I had to multiply F and G. How does that give equation 3.73? I got G as e^{stuff} as in the last bit of equation 3.73. ...
1
vote
0answers
33 views

How to find a function that can approximate another blackbox function programmaticly?

This question has been posted on http://stackoverflow.com/questions/21758016/how-to-find-a-function-that-can-approximate-another-blackbox-function-programmat I was suggested to post it here. I ...
0
votes
1answer
39 views

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 ...
4
votes
6answers
2k 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 ...
0
votes
1answer
88 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 ...
1
vote
0answers
87 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 ...
1
vote
1answer
405 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 ...
3
votes
1answer
92 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?
1
vote
0answers
327 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 ...
4
votes
0answers
137 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. ...