Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [mathematical-modeling]

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

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Bungee Jump (Modelling)

A bungee jumper of mass $m$ attaches a light elastic string to his foot, and the other end to railing of a bridge on which he stands. The string has natural length $l_0$ and modulus of elasticity $\lambda$. Write down the energy equation. (i)To…
Patrick Moloney
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Bound function result - mathematical formulation

excuse me for the quite simple question. Let us assume that we have the function $f(x)=\frac{a-x}{a}$ where $x \in \mathbb{R} $ and $a$ is a scalar. I want to mathematically express that the outcome of the function should belong to the set…
user2276892
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How to start creating Mathematical models?

I know this is a quite general question , but I've always heard about creating mathematical models in economics, social sciences, engineering,... And I would want to know what are the starting points and roadmap to understand what a mathematical…
Fgblanch
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Interpretation of a model

$$ \frac{dx}{dt}=ax(x-b)(1-x)-\frac{xy}{1+cx}$$ $$\frac{dy}{dt}=-ey+\frac{xy}{1+cx}$$ Make a apropriate interpretation of this model. What I thought are: $\frac{dx}{dt}\ \& \ \frac{dy}{dt}$ are the rate of changes of $x$ and $y$, and…
user133140
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Calculating heterozygosity of a population as size increases (combine growth and genetic drift equations)

I am working on a assignment to program a genetic drift simulator and include population growth. My program works fine as far as I can tell, and I have the not unexpected result that in the time I am willing to let my program run, some number of…
Ian Fiddes
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Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials. Factor c1 c2 c3 c4 c5 Factor 1 0.2 0.2 0.2 0.2 0.2 Factor 2 -0.3333 -0.1667 0 0.1667 0.3333 Factor 3 0.25 -0.125 -0.25 -0.125 …
user5216
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Recommendation for resources about forecasting storm surge levels

I have a number of concerns related to storm surge forecasting: A large number of different models have been developed in order to forecast storm surge levels. I've read a lot of papers mentioning the different models they used and their results…
Kurapika
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Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and winter); I have the following seasonal factors…
user76020
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Deriving an Energy Equation

This is an exam problem that I've been doing most of the morning. I'm in college but unfortunately I live 100km away and I don't have anyone to help me and my exam is on Monday. So I'm doing past exam papers and just trying to get as much advice as…
Patrick Moloney
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a mathematical model for file system

We are supposed to come up with a mathematical model describing a file system and its operations. The file system stores metadata in a database, and retrieves it when necessary. How does one go about modelling this in set theory? eg: F : Set of all…
coolharsh55
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Population Growth mathematical modelling?

Hey guys I'm struggling to find much information of modelling single species population dynamics that relates to this question. A question like this is going to be coming up in my final exam and I need to be able to solve it. I'm struggling to even…
Patrick Moloney
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How to represent a decision variable?

I have an association matrix $n\times n$ where the values are either $0$ or $1$. So this matrix is called $B$ and $b(ij)$ is either $0$ or $1$ . However when $i=0$ this means something and if $i>0$ it means something else. How can I express this in…
jhon sari
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Seeking function to model the curve of solutions to $x^y = y^x$

I found a graph of the solutions to the equation $x^y = y^x$ online; the one who posted the graph was curious as to why the set of solutions formed a line and a curve that intersect at the point $(e,e)$. The line of solutions is easy to understand -…
user118534
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Deriving lift equation from scratch

I am trying to derive a model for how the lift of an airplane depends on its speed, surface area of wings, and air density. I used the Buckingham Pi Theorem and some dimensional analysis to come very close to the actual lift equation: $$L=C \times…
BadAtMath
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64 possible values - continuous or discrete?

I have a response variable in a model that is calculated from binary values of an 8x8 grid of pixels, giving a proportion. Technically, there are only 64 possible values the result can take, so would this count as discrete data? There are many…
gisol
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