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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What is a “free parameter” in a computational model?

In many articles regarding computational models of some particular phenomenon, there seems to be a consensus: "the smaller the number of 'free parameters' in the model, the better". So, what is meant by "free parameter", and why is it less desirable…
dnbwise
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Linearize $y=c+ax^b$

This is an exercise from Stefan Heinz Mathematical Modeling: Linearizing $y=ax^b$ is very easy applying log in both sides. But when the constant $c$ appears here I would get $\ln(y-c)=\ln a + b\ln x$. The constant $c$ is to be determined but it…
Lotte
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How do you formulate a vague notion into a mathematical expression?

I am a software engineer wanting to learn math. I also do a little bit of drawing. What I am wondering is, how do you formulate a vague notion of something you're trying to model into a mathematical expression? Here is some background to give you…
Lance
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How can I mathematically model the "building up" of blood pressure during CPR?

In CPR one idea behind chest compressions is that continued compressions lead to a cumulative increase of blood pressure which at some threshold will initiate effective blood circulation throughout the body. One important element though is that any…
Alex Long
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What maths concepts should you know to model infectious diseases?

I'm a high school student and for my math research paper, I've to model and predict spread of an infectious disease (e.g. covid) in a country of my choice. Which math concepts should I know to do this activity? I've heard that I should learn…
ninetysix
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Galerkin projection model reduction exam question.

The following question is from an exam for the course Model Reduction. There are no answers and I don't really know what steps to take. Looking for an expert that can show me how it's done. The viscous Burgers’ equation $$\frac{\partial w}{\partial…
user463102
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Mathematical Modeling of Real-World Situations

I was considering how to model the following problem mathematically and was wondering what you thought the best way to do it is. "A takes 1 minute to cross a bridge, B takes 2 minutes, C takes 5 minutes, D takes 10 minutes. They can cross up to…
JonaGik
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is possible to deduce a formula for vaccination coverage from Whittle threshold theorem?

I am reading the article Application of Whittle’s stochastic threshold theorem to a chickenpox outbreak and I can't understand the meaning of the term "intensity" in the Whittle threshold theorem. In addition, they deduce a formula from Whittle's…
LFRC
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Modelling the number of chess games after n plies

I'm trying to model the number of possible chess games after n plies.(perft results A048987): 1, 20, 400, 8902, 197281, 4865609, 119060324, 3195901860, 84998978956, 2439530234167, 69352859712417, 2097651003696806, 62854969236701747,…
Michael Smith
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Differential Equations & Sinusoidal Functions

I am developing a model for sales forecasting, the basic premise of which is that the rate of change of sales is proportional to the number of possible buyers. In developing this model, I came up with the following ODE, $$\frac{dB}{dt}=k \left(\sin…
user76020
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Which population will benefit most from vaccinating children?

This is from Vynnycky and White's An Introduction to Infectious Disease Modelling. In Population A, children have more contacts than do adults and most of the contacts of children are with other children. In Population B, children have as many…
Sally G
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Shape of a Kite String

A kite is flown at some angle and elevation. Without wind, the string takes the shape of a catenary curve. But the wind is crucial. Is there a name for the shape of a kite string -- is it some other well known curve? And is it easy to model based…
Ed Pegg
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Forced Damped Harmonic Motion: Applied Mathematics

I've been doing this problem for a good while now and just coming to grips with it. I'd like to know if my solution is acceptable. Thanks in advance. A forced and damped harmonic oscillator satisfies $$\ddot{x}+2k\dot{x}+\omega_0^2 x = F\cos\omega…
Patrick Moloney
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Damped Oscillations (Applied Mathematics)

Hey guys I'm doing this exam paper question and I know a quesiton like this will come up. My exam is on Monday I just need someone to check over it and tell me if everything is OK. I'm unable to ask anyone for help. Thanks in advance. A particle…
Patrick Moloney
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Dampened Harmonic Motion (Mathematical Modelling)

Solve the damped harmonic motion system $$\ddot{x} + 2k\dot{x} + \omega^2 x = 0 $$ with initial conditions $\dot{x}= V$ at $x = 0$ in the cases (i) $\omega^2 = 10k^2$ (ii) $\omega^2 = k^2$ (iii) $\omega^2 = 5, k = 3$ Identify the type of…
Patrick Moloney
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