1.DEFINITION
Mathematical modeling uses mathematics as a tool to make predictions about the real world, understand situations, and apply it in making decisions. It can optimize economic growth and can be exploited to understand the Universe and sustain life in adverse conditions. It is used in many fields such as Engineering disciplines and many other fields.
2.ELEMENTS OF A MATHEMATICAL MODEL
Many elements of mathematical models are essential for the formulation, computation, and analysis of complex problems. The elements include the following features:
- Linear equations and defining them
- initial and final boundary conditions in the problem
- classical constraints related to the problem
- major assumptions are taken into account in the problem
3.CLASSIFICATION OF MATHEMATICAL MODELS
Mathematical models comprise relationships and variables. Relationships can be established using operators, arithmetic, algebraic functions, or differential operators. The various structures are discussed now in the following headings.
4.LINEAR AND NON-LINEAR MODEL
If the objective functions and constraints are represented by linear equations,the model is called a linear model. For example, the Linear programming model or LPP model is the most commonly used model in Petroleum and Oil refinery industries. The need to optimize the resources at a minimum cost is needed the most. When the objective functions are represented by linear inequations, the model is non-linear. For example, Simplex method, Dual Simplex, etc.
5.STATIC AND DYNAMIC MODEL
A static model calculates the system problems taking the equilibrium conditions into account. In contrast, the dynamic model accounts for all the changes in the system's state according to time.
6.DISCRETE AND CONTINUOUS MODEL
A discrete model generally refers to the statistical model like the motion of molecules, and its analysis can be considered in this. The continuous model refers to the representation of objects in a continuous manner, for example, the analysis of electric field due to a point charge, fluid in pipe problems, etc.
7.DETERMINISTIC AND PROBABILISTIC MODEL
Deterministic models include certainty; that is it would result in a certain unique result irrespective of any randomness of the system. For example, CPM(CRITICAL PATH METHOD) and EOQ(ECONOMIC ORDER QUANTITY) models are the models which are deterministically used in complex project complex problems and lot size related to inventory control. Probabilistic models are highly uncertain and involve many risks; for example, the PERT(PROGRAMME EVALUATION REVIEW TECHNIQUE) model uses the value of three-time estimates and the beta distribution curve is used for the analysis. This is used in project problems.
8.APPLICATIONS OF MATHEMATICAL MODEL
The various applications of mathematical models can be summarised as follows:
- Used by Engineers to analyze and control a system by building a model of the system and trying out different approaches in simulations by using operators like Boolean algebra and others.
- Estimation of population growth and its analysis is done with the mathematical model techniques.
- Analysis of mechanics problems like Rocket motion analysis.
- Problems of queuing line, waiting line,assembly line problems,transportation and assignment models etc.
- Used in Research and Development programs.
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