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RUBEN DARIO ARISMENDI RUEDA
   CHAPTER 1: ‘MATHEMATICAL MODELING’
Mathematical Modeling, was made to formulate different problems or situations (essential physical systems) into mathematical language by equations that can be treated and solved by many ways. But the most important ways are: Numerical Methods, Graphics results and analytical solutions.
Steps of MathematicalModeling ThenextimagetakenfromPhD. Eduardo Carrillo'spresentation ''METODOS NUMERICOS EN INGENIERIA DE PETROLEOS''
COMPONENTS. ,[object Object]
Independent Variable : Are usually dimensions that determines system's behavior.
Parameters: ''Are refelctive's of the systems properties or composition''
Forcing Functions: External influences acting upon the system ,[object Object]
When Mathematical Models are written in terms of differential rate of change (dv/dt), we can say that we have differential equations as a Model. Example:  Every differential equation will have his own solution by algebraic manipulation or by other kind of techniques when it's not too easy to obtain the exact or analytical solution.
ClassifyingMathematicalmodels. ,[object Object]
Deterministic and probabilistic: A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of initial conditions. Conversely, in a probabilistic model, randomness is present, and variable states are not described by unique values, but rather by probability distributions.,[object Object]
Lumped and distributed parameters: If the model is heterogeneous (varying state within the system) the parameters are distributed. If the model is homogeneous (consistent state throughout the entire system), then the parameters are lumped. Distributed parameters are typically represented with partial differential equations.,[object Object]

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Mathematical modeling