Mathematical modeling

Mathematical modeling

A mathematical model is a representation of a phenomenon in the real world, using mathematical concepts to describe it. This is built for the purpose of questioning in relation to one aspect of the real world.
The formulation of a mathematical model involves:

• Identification of factors (variables) that is specific to the system.
• Establish reasonable assumptions about the system.


In the formulation of hypotheses involving variables change, a reason which they are involved, thus variables that are altered due to other, that is to say, derivatives or differential equations.



CHARACTERISTICS OF A MODEL:
• Diagrams or sketches are for the most part, they represent reality.
• Its main objective is to explain and predict issues of a situation.


NUMERIACAL APPROXIMATION
An approximation is an inexact representation of something that is still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.

ERROR
In science and engineering in general an error is defined as a difference between the desired and actual performance or behavior of a system or object.

ERROR ROUNDING
The rounding error is the loss of mathematical precision that occurs when rounded to the decimal part of a number. It's the difference between the value of the original number and value of the number after you apply the rounding.



ERROS TRUNCATION
Truncation errors are related to the method of approach to be used because they generally face an infinite series of terms, will tend to cut the number of terms, introducing an error at that time, not to use the complete series.



SIGNIFICANT FIGURES
The significant figures of a number are those digits that carry meaning contributing to its precision.


TOTAL NUMBER ERROR
The total numerical error is defined as the sum of the rounding and truncation errors introduced in the calculation.

Bibliography
Javier Aracil Santonja 1986 editorial TECNOS S.A 1986 o’Donnel 27-Madrid -9.
http://www2.uca.es/matematicas/Docencia/2005-2006/FC/0206024/Apuntes/tema1_0506.pdf
http://html.rincondelvago.com/metodos-numericos_5.html
http://www.slideshare.net/nestorbalcazar/mtodos-numricos-03
http://idkernel.sytes.net/MetNum/pdfs/raices2.pdf
http://noosfera.indivia.net/metodos/secante.html
http://es.wikipedia.org/wiki/M%C3%A9todo_de_la_secante
http://www.itescam.edu.mx/principal/sylabus/fpdb/recursos/r45622.PDF