Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations. It describes the Jacobi method, which solves systems by iteratively updating solutions. It also describes Gauss-Seidel method, which improves on Jacobi by using previous updated solutions in the current iteration. Both methods are used to progressively calculate better approximations to the solution until reaching an acceptable level of accuracy.
Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations, including Jacobi, Gauss-Seidel, and Gauss-Seidel relaxation methods. Iterative methods progressively calculate approximations to the solution, unlike direct methods which require completing the full process to obtain the answer. The Jacobi method can solve simple square systems of equations in an iterative fashion. Gauss-Seidel is also an iterative technique that sequentially solves for each unknown using previous approximations. Gauss-Seidel relaxation is similar but incorporates a relaxation parameter. Examples demonstrate applying these methods to solve systems of equations.
This document discusses matrices and their properties. It defines what a matrix is and different types of matrices such as line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also covers operations that can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Properties of these operations are provided.
A borderless classroom? Pocasting in Moodle*1DanHinkley
This document discusses using podcasting in an English language classroom to address issues with the changing teaching context and learner needs. It proposes creating podcasts using free, easy-to-use tools that can be embedded in the course management system for additional practice outside of class. Podcasting has the potential to increase motivation and preparation for assessments by allowing students to access audio examples and practice exams anywhere.
A borderless classroom? Pocasting in MoodleDanHinkley
This document discusses using podcasting in an English language classroom on Moodle. It provides context about the teaching environment, learners, and upcoming changes. Podcasting could address issues like motivation, assessment preparation, and providing further practice. The author chooses PodOmatic for its ease of use and embedding in Moodle. Questions are raised about how podcasting may impact language learning. References on using podcasting for language acquisition are provided.
O documento é uma transcrição da música "You Needed Me" de Anne Murray. Contém as letras da música divididas em várias estrofes que descrevem como a pessoa amada apoiou e deu força ao cantor nos momentos difíceis, dando-lhe dignidade, esperança e fazendo-o se sentir amado. A música exalta como o parceiro esteve sempre presente para enxugar as lágrimas, clarear a mente e comprar de volta a alma do cantor.
This document discusses several numerical methods for finding the roots of equations, including the bisection method, false position method, fixed point method, Newton-Raphson method, and secant method. It provides examples of using these methods to find the maximum deflection of a bookshelf beam and to find a root of the equation x3 - 30x2 + 2400 = 0 using the fixed point method. The document also lists sources used in a bibliography.
Exercises systems of equations for several methodsDUBAN CASTRO
1. The document discusses various numerical methods for solving systems of equations, including: Gauss elimination method, graphical method for 2x2 systems, Thomas algorithm, and Cholesky decomposition method.
2. It provides an example problem of mass balance in a distillation column separating alcohol and water. Equations are set up to solve for the quantities of distillate and residue, as well as the percentage of alcohol recovered in the distillate.
3. The document reviews these numerical methods and provides examples of applying each method to solve systems of equations.
Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations. It describes the Jacobi method, which solves systems by iteratively updating solutions. It also describes Gauss-Seidel method, which improves on Jacobi by using previous updated solutions in the current iteration. Both methods are used to progressively calculate better approximations to the solution until reaching an acceptable level of accuracy.
Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations, including Jacobi, Gauss-Seidel, and Gauss-Seidel relaxation methods. Iterative methods progressively calculate approximations to the solution, unlike direct methods which require completing the full process to obtain the answer. The Jacobi method can solve simple square systems of equations in an iterative fashion. Gauss-Seidel is also an iterative technique that sequentially solves for each unknown using previous approximations. Gauss-Seidel relaxation is similar but incorporates a relaxation parameter. Examples demonstrate applying these methods to solve systems of equations.
This document discusses matrices and their properties. It defines what a matrix is and different types of matrices such as line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also covers operations that can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Properties of these operations are provided.
A borderless classroom? Pocasting in Moodle*1DanHinkley
This document discusses using podcasting in an English language classroom to address issues with the changing teaching context and learner needs. It proposes creating podcasts using free, easy-to-use tools that can be embedded in the course management system for additional practice outside of class. Podcasting has the potential to increase motivation and preparation for assessments by allowing students to access audio examples and practice exams anywhere.
A borderless classroom? Pocasting in MoodleDanHinkley
This document discusses using podcasting in an English language classroom on Moodle. It provides context about the teaching environment, learners, and upcoming changes. Podcasting could address issues like motivation, assessment preparation, and providing further practice. The author chooses PodOmatic for its ease of use and embedding in Moodle. Questions are raised about how podcasting may impact language learning. References on using podcasting for language acquisition are provided.
O documento é uma transcrição da música "You Needed Me" de Anne Murray. Contém as letras da música divididas em várias estrofes que descrevem como a pessoa amada apoiou e deu força ao cantor nos momentos difíceis, dando-lhe dignidade, esperança e fazendo-o se sentir amado. A música exalta como o parceiro esteve sempre presente para enxugar as lágrimas, clarear a mente e comprar de volta a alma do cantor.
This document discusses several numerical methods for finding the roots of equations, including the bisection method, false position method, fixed point method, Newton-Raphson method, and secant method. It provides examples of using these methods to find the maximum deflection of a bookshelf beam and to find a root of the equation x3 - 30x2 + 2400 = 0 using the fixed point method. The document also lists sources used in a bibliography.
Exercises systems of equations for several methodsDUBAN CASTRO
1. The document discusses various numerical methods for solving systems of equations, including: Gauss elimination method, graphical method for 2x2 systems, Thomas algorithm, and Cholesky decomposition method.
2. It provides an example problem of mass balance in a distillation column separating alcohol and water. Equations are set up to solve for the quantities of distillate and residue, as well as the percentage of alcohol recovered in the distillate.
3. The document reviews these numerical methods and provides examples of applying each method to solve systems of equations.
Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations, including Jacobi, Gauss-Seidel, and Gauss-Seidel relaxation methods. Iterative methods progressively calculate approximations to the solution, unlike direct methods which require completing the full process to obtain the answer. The Jacobi method is used to solve simple square systems of equations. Gauss-Seidel is an iterative technique that solves systems of linear equations by computing updated solutions sequentially using forward substitution. Gauss-Seidel relaxation is similar but incorporates a relaxation parameter. Examples demonstrate applying these methods over multiple iterations to solve systems.
The document discusses the method of simple Gauss elimination for solving systems of linear equations. It has two phases: elimination of unknowns and back substitution. The method works by performing elementary row operations like multiplying rows by constants and subtracting rows from each other to eliminate variables. An example problem is worked through step-by-step to demonstrate the method. Potential issues like rounding error, division by zero, and ill-conditioned systems are also discussed.
Este documento define y explica los conceptos básicos de las matrices, incluyendo su historia, definición, tipos (fila, columna, rectangular, triangular), operaciones (suma, resta, multiplicación por escalar, multiplicación), propiedades (asociatividad, conmutatividad, distribución), determinantes, matrices traspuestas e inversas, y matrices simétricas. También proporciona ejemplos ilustrativos de cada uno de estos conceptos.
The document discusses Taylor series, which represent a function as an infinite sum of terms calculated from the function's derivatives at a single point. Taylor series can approximate functions using a finite number of terms. Specifically, the Taylor series of a function f(x) centered at a value a is the power series involving the derivatives of f evaluated at a. If the series is centered at zero, it is called a Maclaurin series. An example calculates the Maclaurin polynomial P3(x) to approximate the arccos(x) function.
Exercises systems of equations for several methodsDUBAN CASTRO
1. The document discusses various numerical methods for solving systems of equations, including: Gauss elimination method, graphical method for 2x2 systems, Thomas algorithm, and Cholesky decomposition method.
2. It provides an example problem of mass balance in a distillation column separating alcohol and water. Equations are set up to solve for the quantities of distillate and residue, as well as the percentage of alcohol recovered in the distillate.
3. The document reviews these numerical methods and provides examples of applying each method to solve systems of equations.
The Muller method is a root-finding algorithm that estimates the root of a function by fitting a parabola through three points on the graph of the function. It works by first calculating the coefficients of a parabola that passes through three given points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)). Then, the x-value where this parabola intersects the x-axis gives an estimated root. This process is repeated iteratively to converge on an accurate root. The document provides mathematical definitions of the Muller method and an example application with coefficients h = 0.1, x2 = 5, and x1 = 5.
This document discusses several numerical methods for finding roots of equations, including the bisection method, false position method, fixed point method, Newton-Raphson method, and secant method. It provides an example of using the Newton-Raphson method to find the maximum deflection of a bookshelf beam. It also asks which function could be used with the fixed point method to find a root between 10 and 15 for the equation x3 - 30x2 + 2400 = 0. Finally, it provides an example of using the bisection method to find the root of the equation f(x)=3x+sinx-ex.
This document discusses roots of polynomials. It defines polynomials and monomials, and explains that the roots of a polynomial are the values that make the polynomial equal to zero. It covers the fundamental theorem of algebra, which states that a polynomial of degree n has n roots. Descartes' rule for the number of positive roots is introduced. Properties of the roots and factors of polynomials are outlined. Examples of finding the roots of polynomials are provided at the end.
This document discusses methods for calculating the roots of equations. It introduces the bisection method, method of successive approximations, and Newton's method. The bisection method involves taking an interval where the function changes signs and iteratively bisecting the interval to converge on a root. The method of successive approximations generates a sequence of approximations that converge to a root if the derivative is less than 1. Newton's method uses the tangent line approximation at each step to quickly converge on roots.
La Ley de Darcy describe el flujo de fluidos a través de medios porosos. Henry Darcy realizó un experimento donde midió la velocidad de flujo de agua a través de arena dentro de una tubería horizontal y encontró que la velocidad es directamente proporcional a la diferencia de presión entre los extremos e inversamente proporcional a la longitud de la tubería y la viscosidad del fluido. La Ley de Darcy se utiliza comúnmente en ingeniería petrolera para calcular la permeabilidad de yacimientos.
This document discusses numerical methods and their application in reservoir simulation. It defines numerical methods as procedures that can solve mathematical problems that are difficult to solve using traditional analytical methods. It also discusses numerical approximation, significant figures, error, Taylor series, numerical simulation, and the history and recent advances in reservoir simulation.
Solution of equations for methods iterativosDUBAN CASTRO
This document discusses iterative methods for solving systems of equations, including Jacobi, Gauss-Seidel, and Gauss-Seidel relaxation methods. Iterative methods progressively calculate approximations to the solution, unlike direct methods which require completing the full process to obtain the answer. The Jacobi method is used to solve simple square systems of equations. Gauss-Seidel is an iterative technique that solves systems of linear equations by computing updated solutions sequentially using forward substitution. Gauss-Seidel relaxation is similar but incorporates a relaxation parameter. Examples demonstrate applying these methods over multiple iterations to solve systems.
The document discusses the method of simple Gauss elimination for solving systems of linear equations. It has two phases: elimination of unknowns and back substitution. The method works by performing elementary row operations like multiplying rows by constants and subtracting rows from each other to eliminate variables. An example problem is worked through step-by-step to demonstrate the method. Potential issues like rounding error, division by zero, and ill-conditioned systems are also discussed.
Este documento define y explica los conceptos básicos de las matrices, incluyendo su historia, definición, tipos (fila, columna, rectangular, triangular), operaciones (suma, resta, multiplicación por escalar, multiplicación), propiedades (asociatividad, conmutatividad, distribución), determinantes, matrices traspuestas e inversas, y matrices simétricas. También proporciona ejemplos ilustrativos de cada uno de estos conceptos.
The document discusses Taylor series, which represent a function as an infinite sum of terms calculated from the function's derivatives at a single point. Taylor series can approximate functions using a finite number of terms. Specifically, the Taylor series of a function f(x) centered at a value a is the power series involving the derivatives of f evaluated at a. If the series is centered at zero, it is called a Maclaurin series. An example calculates the Maclaurin polynomial P3(x) to approximate the arccos(x) function.
Exercises systems of equations for several methodsDUBAN CASTRO
1. The document discusses various numerical methods for solving systems of equations, including: Gauss elimination method, graphical method for 2x2 systems, Thomas algorithm, and Cholesky decomposition method.
2. It provides an example problem of mass balance in a distillation column separating alcohol and water. Equations are set up to solve for the quantities of distillate and residue, as well as the percentage of alcohol recovered in the distillate.
3. The document reviews these numerical methods and provides examples of applying each method to solve systems of equations.
The Muller method is a root-finding algorithm that estimates the root of a function by fitting a parabola through three points on the graph of the function. It works by first calculating the coefficients of a parabola that passes through three given points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)). Then, the x-value where this parabola intersects the x-axis gives an estimated root. This process is repeated iteratively to converge on an accurate root. The document provides mathematical definitions of the Muller method and an example application with coefficients h = 0.1, x2 = 5, and x1 = 5.
This document discusses several numerical methods for finding roots of equations, including the bisection method, false position method, fixed point method, Newton-Raphson method, and secant method. It provides an example of using the Newton-Raphson method to find the maximum deflection of a bookshelf beam. It also asks which function could be used with the fixed point method to find a root between 10 and 15 for the equation x3 - 30x2 + 2400 = 0. Finally, it provides an example of using the bisection method to find the root of the equation f(x)=3x+sinx-ex.
This document discusses roots of polynomials. It defines polynomials and monomials, and explains that the roots of a polynomial are the values that make the polynomial equal to zero. It covers the fundamental theorem of algebra, which states that a polynomial of degree n has n roots. Descartes' rule for the number of positive roots is introduced. Properties of the roots and factors of polynomials are outlined. Examples of finding the roots of polynomials are provided at the end.
This document discusses methods for calculating the roots of equations. It introduces the bisection method, method of successive approximations, and Newton's method. The bisection method involves taking an interval where the function changes signs and iteratively bisecting the interval to converge on a root. The method of successive approximations generates a sequence of approximations that converge to a root if the derivative is less than 1. Newton's method uses the tangent line approximation at each step to quickly converge on roots.
La Ley de Darcy describe el flujo de fluidos a través de medios porosos. Henry Darcy realizó un experimento donde midió la velocidad de flujo de agua a través de arena dentro de una tubería horizontal y encontró que la velocidad es directamente proporcional a la diferencia de presión entre los extremos e inversamente proporcional a la longitud de la tubería y la viscosidad del fluido. La Ley de Darcy se utiliza comúnmente en ingeniería petrolera para calcular la permeabilidad de yacimientos.
This document discusses numerical methods and their application in reservoir simulation. It defines numerical methods as procedures that can solve mathematical problems that are difficult to solve using traditional analytical methods. It also discusses numerical approximation, significant figures, error, Taylor series, numerical simulation, and the history and recent advances in reservoir simulation.
9. 2.FALSE POSITION The same procedure is continued that the bisection method, to exception of the change in the form of finding xr. 4
10.
11. The xi value is determined knowing the graph of the function (Mathematics of Microsoft or Excel).
12. When it is xi with g(xi), g(xi)=xi+1, that is to say it will be the value to evaluate.
13. If the function doesn't converge the method of clearances of x it is used, the times that it is necessary until the approximate value of g(x) it is similar to that of the f(x root).
14. The first one is evaluated derived in the point to evaluate, if it is gives smaller than 1, it converges, if it is gives bigger it diverges.5