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Mathematical Model, Data Modeling, Mathematics Assignment Help
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>> Mathematical Model, Data Modeling
Mathematical model is a description of a system by using mathematical language and concepts. The process of developing a mathematical model is known as mathematical. Mathematical models are mainly used not only in the natural sciences for example biology, physics, meteorology, earth science and engineering disciplines for example artificial intelligence, computer science but also in the social sciences for example psychology, economics, political science and sociology and physicists, statisticians , engineers, , operations analysts and economists use these mathematical models mostly..
Mathematical models can be divided in many forms, including but not limited to statistical models, dynamical systems, game theoretic models and differential equations. These and many other types of models can overlap, with a given model involving a variety of abstract structures. In short, mathematical models can include logical models, as far as logic is taken as a part of mathematics.
Mathematical models may be classified in the following ways:
1. Linear and Nonlinear:
Mathematical models are generally composed by variables, that are abstractions of quantities of interest in the given systems, and operators which act on these variables, which may be functions, algebraic operators, differential operators, etc. In case all the operators in a mathematical model exhibit linearity, the resulting mathematical model is known as linear. A mathematical model is considered to be nonlinear other cases.
The question of nonlinearity and linearity is dependent on context, and the linear models can have nonlinear expressions in them. In a statistical linear model, it is considered a linear relationship in the parameters, but it may be nonlinear in the predictor variables. A differential equation is known to be linear if it is written with linear differential operators, but it may still have nonlinear expressions in it. In a mathematical programming model, if the constraints and objective functions are represented entirely by linear equations, then the model is considered as a linear model. If one or many of the objective functions or constraints are shown with a nonlinear equation, then the model is considered as a nonlinear model.
Nonlinearity is a simple system, also associated with phenomena such as irreversibility and chaos.
2. Deterministic and Probabilistic (Stochastic):
A deterministic model is known in which every set of variable states is uniquely described by parameters in the model and by sets of previous states of these variables. Thus, deterministic models perform the same way for a given set of initial conditions. In other word, in a stochastic model, randomness is present, and variable states are not described by unique values, but rather by probability distributions.
3. Static and Dynamic:
A static model does not have time element, while a dynamic model does. Dynamic models mainly are represented with difference equations or differential equations.
4. Discrete and Continuous:
A discrete model does not take function of time and usually uses time-advance methods, while a Continuous model does. Continuous models typically are represented with f(t) and the changes are reflected over continuous time intervals.
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