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Mathematical modeling is the art of capturing natural phenomenon of real life in the mathematical equation. For example the reading of bike speedometer shows 70 km/hr. There are ways through which we can develop a mathematical model. The process for developing a mathematical model is as follows:
1. Finding a real world problem.
2. Formulating a mathematical model of the problem, identifying variables and establishing hypotheses simple to be treated mathematically.
3. Applying the mathematical knowledge that you have to reach mathematical conclusions.
4. Comparing the data obtained as predictions with real data. If the data are different, the process is restarted.
The mathematical modeling is divided into two models, discrete and continuous model.
Discrete model: A discrete model treats objects as discrete, such as the particles in a molecular model. A clock is an example of discrete model because the clock skips to the next event start time as the simulation proceeds.
Continuous Model: A continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe or channels, temperatures and electric field. Although there are some limitations of mathematical modeling. Till today many mathematical modeling have been developed and applied successfully to understand and get an insight into thousands of situations. Sone of the subjects like mathematical physics, mathematical economics, operation research etc are synonyms with mathematical modeling.
The major courses to study in mathematical modeling are Differential equation based models, Dimensional analysis, Stochastic models, Partial differential equations, stiff equations, delay differential equations, Compartment models: population dynamics, infectious disease models, Model scaling, dimensionless forms and ?-numbers, Probability distribution, random draws from distributions, Central limit theorem etc.
The major courses to study in mathematical modeling are Differential equation based models, Dimensional analysis, Stochastic models, Partial differential equations, stiff equations, delay differential equations, Compartment models: population dynamics, infectious disease models, Model scaling, dimensionless forms and ?-numbers, Probability distribution, random draws from distributions, Central limit theorem etc.
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