martes, 27 de julio de 2010
Linear System of Equations and MATRICES
A linear system of equations is a set of linear equations variables. Linear systems can be represented in matrix form as the matrix equation
Ax = B
where A is the matrix of coefficients, x is the column vector of variables, and B is the column vector of solutions.
Each equation in the system becomes a row. Each variable in the system becomes a column. The variables are dropped and the coefficients are placed into a matrix. If the right hand side is included, it's called an augmented matrix. If the right hand side isn't included, it's called a coefficient matrix.
The system of linear equations ...
x + y - z = 1
3x - 2y + z = 3
4x + y - 2z = 9
becomes the augmented matrix
Now, in order to understand how to solve matrices, you need to know some terms related to this topic:
Finally, some facts about matriz definition!!!
lunes, 26 de julio de 2010
jueves, 22 de julio de 2010
Roots of Equations!
A root or solution of equation f(x)=0 are the values of x for which the equation holds true.
Methods for finding roots of equations are basic numerical methods. There are 3 ways to find the roots of equations:
Methods for finding roots of equations are basic numerical methods. There are 3 ways to find the roots of equations:
Graphical Method is very simple!! The main idea is to make a plot of the function and observe where it crosses the X axis. This method is not very accurate and is difficult when you don't have an idea about the interval where the root is located.
Bracketing and Open Methods are clasified:
There are some differences between these two fundamental Approaches. In the left side, Closed Methods features; in the right side Open Methods comparison.
miércoles, 21 de julio de 2010
Some Facts About Taylor Series....
Taylor series can be used to evaluate the value of a whole function in each point, if the functional value and its derivatives are identified at single point.
Uses of the Taylor series for whole functions are:
1.The sum of partial series can be used as approximations of the entire function.
2.The representation of series reduces many mathematical proofs.
In Taylor series, algebraic functions are indicated using an algebraic equation, and transcendental functions are indicated using properties which holds them, namely differential equation. Example the exponential function is equal to its own derivative and its original value is 1.
Taylor series is a expansion of series and its function about a point.
Something about Errors!!!
Errors are very important in engineering!!! ACCURACY is vital!
They are defined as "The difference between an observed value and the true value of a quantity" And it´s very important to notice how representative are they...
Do you know what types of error are there???
But talking about the practice, the most common definitions are Relative Approximate Error....
And True Error:
I'm sure this will be very usefull comparing the numerical methods!....
viernes, 9 de julio de 2010
lunes, 24 de mayo de 2010
An interesting Book to our career.......
In this link, you are going to find the book called "The Mathematics of Reservoir Simulation" .
As we all know, Simulation is one of the biggest oportunities to describe the reservoir behaviour. Using computer models, engineers can predict the flow of fluids on the porous media. Is a huge tool for reservoir management, these models can provide important information for the future field development....
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