RAICES DE ECUACIONES

This problems are related with one variable valor our parameter that satisfy some equation. Then are useful in engineering problems when are impossible find parameters from some equations with analytic techniques.
Is Y= f(x). The x values who carry that y=0 are called, equations raiz. Algebra theorem says that all polynomials from n grade have n raiz. In the real raiz, we can say tally with x values whose the function cut the abcises axis.
The polynomial raiz maybe real’s our complex. If a polynomial had coefficients: coefficients ---a0, a1, a2,… an-1, --- an real’s, however all complex raiz always will be in complex conjugate pars . For example, Cubic polynomial has the next form:
f(x)=aox3+a1x2+a2x+a3
Fundamental algebra theorem says that someone n grade polynomial, have n raiz. In cubic polynomial case we can obtain:
-3 real raiz diferents.
-1 real raiz with multiplicity 3.
-1 simple real raíz and 1 real raiz with multipliciy 2.
-1 real raiz and a complex conjugated pair
The methods to find the real raiz from algebraic equations have to method: interval method and opened method. This presentation don’t want explain every one of methods but we will classified and designated.

Referencias
*"Modelos, métodos numéricos y computadoras", Jorge Icaro Condado Jauregui, Notas del instituto de Investigación en ciencias matemáticas

*http://www.uv.es/diazj/cn_tema2.pdf
*http://www.acatlan.unam.mx/acatlecas/mn/MN_02.htm

Numeric Approximation

Introduction

In numeric analysis, the mistake between the real valor and the valor securer is called: approximation error, to reduce these errors effects, we need to do numeric approximations which have some properties that help us to reduce the approximation error.

Numeric Approximation:

Then are techniques through a mathematical model are solved using arithmetic calculus.
The numeric approximation be systematic techniques whose the results be approximation from the true valor that take on the interest variant; constant repetition of the technique (iteration), enable come nearly to the want valor.
We can understand by numeric approximation X* a quantity that represent a number whose exactly valor is X. When the number X* is nearly to the most exactly X valor, will be a better approximation from this number. Examples:
3.1416 is a numeric approximation from p,
2.7183 is a numeric approximation from e,
1.4142 is a numeric approximation from Ö2, and
0.333333 is a numeric approximation from 1/3.

Significant amount:
The number of significant amounts is the number of digit t, that we can use, con trust, when we measure a variable.
The ceros included in a number not ever are significant amount; for example the numbers:
-0.00002415
-0.002415
-2415
-241500

Exactness and precision:
Precision refer the significant amount numbers whose represent a quantity.
The exactness refers at the number approximation our some measure from numeric valor whose supposes represent.
Example: p is irracional number constituted by infinite amounts numbers; 3.141592653589793... is good approximation of p, that could be considerate the exact valor. If we considered the next p approximation, we can say:
p = 3.15 not have precision and are inexact
p = 3.14 not have precision but are exact
p = 3.151692 have precision but are inexact
p = 3.141593 have precision and are exact

Numeric methods should offer exactly solutions and precise. Mistake term is used to refer the inexactly so measure the bad precision in predictions.

Mistakes
When we make numeric approximations, could generate some mistake type when we work with operations and mathematical quantity:
-Un-continuity mistakes: result from the approximation use.
-Round mistakes: result from use a finite quantity of significant amount.

Them are some numeric approximation methods, we designated, but we won’t study them in this blog:
1 Euler
2 Taylor’s methods
3 Runge-Kutta’ method
4 Matlab simulation

Refers:

-UNIVERSIDAD SIMON BOLIVAR, División de Ciencias Físicas y Matemáticas, Departamento de Computo Científico
-Sergio Ramírez, hellnight39@hotmail.com
-http://www.google.com.co/url?sa=t&source=web&ct=res&cd=1&ved=0CBYQFjAA&url=http%3A%2F%2Fdcb.fi-c.unam.mx%2Fusers%2Fgustavorb%2FMN%2FPresentaciones%2F1.2%2520Aproximacion%2520numerica.pps&rct=j&q=Aproximaci%C3%B3n+Num%C3%A9rica&ei=XEfrS8CuIYbGlQf42KCcBA&usg=AFQjCNF18xIiVt1us5qIJ1OqbfB7WdIMNw&sig2=kn3-mqXu9JNVnmlEVNfdUQ, Gustavo Rocha 2005.

About The Gulf of Mexico accident

About The Gulf of Mexico accident

All people and news magazines speak about the ecological disaster in the Gulf of Mexico produced by the Deepwater Horizon platform, all world want a benefice from BP our other emprises involucrate in the platform disaster.
Now, the giant fight is coming: some involucrate emprises try to responsibility one to another, the people from Gulf don’t have anything to fish, and the drilling operation stopped in the Gulf of Mexico (the scare to offshore exploration live in all seas) some one of the most important hydrocarbons production areas.
Everyone say about the disaster in ambient theme, people say about the thousands of animals that die or suffer the consequences of the petroleum in the sea and costs, but the real responsible all we have. When we run in a car, when we buy a detergent, when we chew a gum, when we…, in general, the oil is present in the most important products and service that we use daily, we can’t replace this component in our life’s without jeopardize the economic personal an global; for all them, the people need to know: WE NEED THE OIL, and the society responsibility is help with solutions and not obstruct the engineering works.

The offshore works are very difficult, and responsibility from the oil engineers is very high, how you can see, their lives are dangerous, and the people don’t know that all petroleum industry people who work in exploration and oil production, works with attempt information (the engineer can’t see bottom hole), and the accidents are daily in a oil camp, but the engineer are who works all day in them, however the accident happen, and everyone are responsible from them.
With the stopped drilling operations, the people wants decrease the oil offer, but we knows the demand increase, with them the oil price increase too; if we stand out that the Gulf Mexico is some of the more important oil production areas, our going to see that stopping the oil drilling, more unemployed (from oil industry and service employed) and oil unsupplied will be.
The people need to know the accidents occur, the oil industry is very complicated, and nobody wants the ecosystem destruction; the people have to help with ideas and don’t obstruct with bad critical to solve this problem come in harmony with nature and the society needles.

MODELS

SOME BASIC CONCEPTS

Sistem concept have diferents definitions among which are:

-Components collection organized to accomplish a function or set of functions [1].

-Set of cohesive entities pursuing a specific goal [2].

-Entity that maintains its existence through the interaction of its parts [3].

Model definition has multiple references about them too, among which are:

-Physic representation, mathematic or about logic type, from system, entity, phenomena or process [1].

-Representation of a real system that is equivalent to this system in all aspects respects [2]

-Simplified representation of a system from a particular viewpoint in time and space to provide an understanding of the real system [3]

-Representation of the construction and operation of some system of interest [4]

-Description logic of how a system, process or component works [5].

The models maybe physics, when show at scale the physic properties from the real system, graphics, when build graphics diagrams that describe the structure high level about system operation, or mathematics, when a set of mathematical or logical expressions which express the relations between the entities of the system.

A simple mathematical model can be defined as a formulation or equation that expresses the essential characteristics of a physical system or process in mathematical terms.
Can be represented by a functional relationship of the form:

Dependent Variable = f (independent variables, parameters, depending on strength)

In where:


· The dependent variable is: a feature that reflects the state or system behavior.

· The independent variables are generally as space and time dimensions, through which the system behavior will be determined.

·Parameters: they are reflections of the properties system or system composition.

·The force functions: the external influences acting on the system.

·The f function: can be an algebraic expression or a huge and complicated set of differential equations.*

It should be noted that mathematical models can be solved by analytical methods or numerical methods. The analytic solution of a mathematical model consists in obtaining an expression which can be calculated to obtain exact values of the output variables that interest us. The numerical methods of solving mathematical models are based on the discretization and approximation of the numerical values of model variables, generally conditioned by the discretization of the independent variables (usually time and or space).

MODELS TIPES

Mathematical models of any system can be:

-Static or dynamic.
-Continuous or discrete.
-Deterministic or random.

Static models are those time-invariant and dynamic, by contrast, considered the temporal variation of the state of the modeled system.

Continuous models work in the system state variables modeled as continuous variables in terms of working time or performance of the system while discrete models (or discrete event models) consider only actions or events characteristic of the simulated system for those who do not take into account their evolution, but only the moment of its consummation.

REFERENCES

1.- DoD Glossary of M&S Terms. (DoD 5000.59-M). December 1997.
2.- Cunningham, Conrad H. “Lecture Notes of CSci405: Computer Simulation”. Department of Computer and Information Science, University of Mississippi, 2000.
3.- Bellinger, Gene. “Modeling & Simulation”. Outsights Corp., 1997.
4.- Maria, Anu. “Introduccion to Modeling and Simulation”. State University of New York at Binghamton. Proceeding of the 1997 Winter Simulation Conference.
5.- Diamond, Bob. “Concepts of Modeling and Simulation”, Imagine That Inc., 1997.

Prof. Dr. J. A. Capote; Dr. D. Alvear; Dr. O. Abreu; Ing. Ind. M. Lázaro; Ing. Ind. P. Espina.
“Algunos Conceptos y Definiciones del Modelado y Simulación Computacional de Incendios” Grupo GIDAI – Seguridad contra Incendios – Investigación y Tecnología. UNIVERSIDAD DE CANTABRIA, 2006.

*Jorge Icaro Condado Jauregui. “Modelos métodos numéricos y computadoras”, Notas del instituto de investigación en ciencias matemáticas, 2010.