Mathematical modelling


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Mathematical modelling

  1. 1. A mathematical model is the mathematicaldescription of a real situation.In developing the model, someassumptions are made and we considersome simplifications of reality.A model can represent it using:• Relations• functions
  2. 2. There are three types of models:•Linear model: We calllinear models to situationscan be represented by alinear function. can bedetermined graphically orby means of an equation.
  3. 3. • Quadratic model: We say that the model is quadratic if we can express by means of a quadratic function. A quadratic model can be determined through an equation or by means of a graph that made the best approximates of the data.
  4. 4. • Exponential model: We call exponential models to situations that are represented by an exponential function. The exponential models are very common in the study of population increases, the calculation of bank interest, so as various physical phenomena.
  5. 5. The process for develop a mathematical model is asfollowing: 4.Compare the data obtained as predictions with real data. If the data are different, the process is restarted.
  6. 6. A single differential equation mathematicalmodel can be of many different phenomena. a mathematical model is formed by an initialvalue problem, or also value problem at theborder.
  7. 7. • An analysis of the spread of a contagious flu, for example, is reasonable to assume that the rate or reason that spreads not only is proportional to the number of people, x (t), which have contracted at time t, but also the number of subjects, and (t), which have not yet been exposed to infection. If the rate is dx / dt, then• Where k is the usual constant of proportionality.
  8. 8. • If, for example, introduces an infected person in a constant population of n people, then x and y are related by x + y = n + 1. We use this equation to eliminate and in equation (1) and obtain the model• An obvious initial condition accompanying equation (2) is x (0) = 1.