Numerical Methods

Numerical Methods are techniques by which mathematical problems can be formulated in such a way tha can be solved using arithmetic.The numerical analysis to devise methods to " aproximate" efficiently solutions to problems espressed mathematically. The Main objective of numerical analysis is to find solutions " approximate" to complex problems using only the simplest operations.

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Mathematicals Model

Mathematical Approximation

Roots of Equations

MATHEMATICALS MODELS

In the first place we can define a Mathematical Model as a formulation or equation that expresses the main features of a Physical system or a Process in Mathematical terms.

Mathematical models are used particularly in natural sciences and engineering disciplines ( Physics, Biology, Meteorology, and Electrical Engineering) but also in social sciences ( Economics, Sociology and Political Science), physicists, engineers, computer scientists,and economists use mathematicals models mos extensively.

Mathematical models can take many forms,including but not limited dynamical systems, statistical models, differential equations, or game - theoretical models. These and other types of models can overlap with a given model involving a variety of abstract structures.

In General the model can be represented with the next functional relationship :

dependent variable = f (independent variable, parameters, forcing functions)

The dependent Variable is a feature that usually represent the behaviour or system's state, the Independents variables are dimensions as the time and space through which is determinate the system's behaviour. The Parameters are reflective of properties or system's composition. Finally the forcing functions are external influences acting upon the system.

we can obtain analytical or numerical solutions of a problem.The Firsts usally are accurate and the latter are aproximate.

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