Classification of singularity
•Download as PPTX, PDF•
0 likes•680 views
This document discusses power series and the classification of singularities. It defines power series as an infinite series involving terms of the form (x - x0)k. Singular points are points where a function is not analytic, meaning it does not have a convergent Taylor series. Singular points are classified as regular singular points if (x - x0)P(x) and (x - x0)2Q(x) are analytic, or irregular singular points if they are not analytic.
Report
Share
Report
Share
Recommended
Ch05 4
The document discusses regular singular points of differential equations. A point x0 is a regular singular point if the functions P, Q, and R are analytic at x0 or their limits exist and are finite as x approaches x0. Several examples are provided to illustrate regular singular points, including the Bessel and Legendre equations. An irregular singular point is defined as one where these limits do not exist. The behavior of solutions near regular singular points can be analyzed using power series methods.
Ch05 3
The document discusses series solutions to ordinary differential equations near ordinary points. It defines ordinary and singular points, and states that if the point is ordinary, then the solutions can be expressed as power series expansions with a radius of convergence at least as large as that of the coefficients' power series. Several examples are worked through to demonstrate finding the radius of convergence of the series solutions.
Series solutions at ordinary point and regular singular point
The document discusses series solutions for second order linear differential equations near ordinary and regular singular points.
It defines an ordinary point as a point where the functions p(x) and q(x) in the normalized form of the differential equation are analytic. Near an ordinary point, there exist two linearly independent power series solutions of the form Σcn(x-a)n that converge within the radii of convergence of p(x) and q(x).
It also discusses finding series solutions near a regular singular point x0=0, where the limits of p(x) and q(x) as x approaches 0 exist. An initial guess of a power series solution with exponent r is made, and the
160280102042 c3 aem
This document discusses methods for finding series solutions to differential equations, namely the power series method and Frobenius method. It first introduces the concepts of ordinary and singular points. Then it explains how to apply the power series method to find a series solution for ordinary points by assuming the solution is a power series and equating coefficients. Next, it describes how the Frobenius method extends the power series method to find solutions near singular points by using the indicial equation and recurrence relations. It outlines the three cases for the indicial roots that determine the final form of the solutions.
Solution of Differential Equations in Power Series by Employing Frobenius Method
In this tutorial, we discuss about the solution of the differential equations in terms of power series. All the cases associated with this attachment has been discussed
Power series
Series solution of ordinary differential equation
advance engineering mathematics
The power series method is the standard method for solving linear ODEs with variable
coefficients. It gives solutions in the form of power series. These series can be used for computing values, graphing curves, proving formulas, and exploring properties of
solutions, as we shall see.
Series solution to ordinary differential equations
This document discusses power series solutions and the Frobenius method for solving ordinary differential equations with variable coefficients. It explains that power series can be used to find solutions around ordinary points, while the Frobenius method extends this approach to regular singular points through generalized power series involving an index term. The Frobenius method involves making an ansatz for the solution as a power series with an unknown index, then determining the index and coefficients by substituting into the differential equation and setting terms of different powers of x equal to zero.
Ch05 2
The document discusses series solutions to second order linear differential equations near ordinary points. It provides an example of finding the series solution to the differential equation y'' + y = 0 near x0 = 0. The solution is found to be a cosine series which represents the cosine function, a fundamental solution. A second example finds the series solution to Airy's equation near x0 = 0, obtaining fundamental solutions related to Airy functions.
Recommended
Ch05 4
The document discusses regular singular points of differential equations. A point x0 is a regular singular point if the functions P, Q, and R are analytic at x0 or their limits exist and are finite as x approaches x0. Several examples are provided to illustrate regular singular points, including the Bessel and Legendre equations. An irregular singular point is defined as one where these limits do not exist. The behavior of solutions near regular singular points can be analyzed using power series methods.
Ch05 3
The document discusses series solutions to ordinary differential equations near ordinary points. It defines ordinary and singular points, and states that if the point is ordinary, then the solutions can be expressed as power series expansions with a radius of convergence at least as large as that of the coefficients' power series. Several examples are worked through to demonstrate finding the radius of convergence of the series solutions.
Series solutions at ordinary point and regular singular point
The document discusses series solutions for second order linear differential equations near ordinary and regular singular points.
It defines an ordinary point as a point where the functions p(x) and q(x) in the normalized form of the differential equation are analytic. Near an ordinary point, there exist two linearly independent power series solutions of the form Σcn(x-a)n that converge within the radii of convergence of p(x) and q(x).
It also discusses finding series solutions near a regular singular point x0=0, where the limits of p(x) and q(x) as x approaches 0 exist. An initial guess of a power series solution with exponent r is made, and the
160280102042 c3 aem
This document discusses methods for finding series solutions to differential equations, namely the power series method and Frobenius method. It first introduces the concepts of ordinary and singular points. Then it explains how to apply the power series method to find a series solution for ordinary points by assuming the solution is a power series and equating coefficients. Next, it describes how the Frobenius method extends the power series method to find solutions near singular points by using the indicial equation and recurrence relations. It outlines the three cases for the indicial roots that determine the final form of the solutions.
Solution of Differential Equations in Power Series by Employing Frobenius Method
In this tutorial, we discuss about the solution of the differential equations in terms of power series. All the cases associated with this attachment has been discussed
Power series
Series solution of ordinary differential equation
advance engineering mathematics
The power series method is the standard method for solving linear ODEs with variable
coefficients. It gives solutions in the form of power series. These series can be used for computing values, graphing curves, proving formulas, and exploring properties of
solutions, as we shall see.
Series solution to ordinary differential equations
This document discusses power series solutions and the Frobenius method for solving ordinary differential equations with variable coefficients. It explains that power series can be used to find solutions around ordinary points, while the Frobenius method extends this approach to regular singular points through generalized power series involving an index term. The Frobenius method involves making an ansatz for the solution as a power series with an unknown index, then determining the index and coefficients by substituting into the differential equation and setting terms of different powers of x equal to zero.
Ch05 2
The document discusses series solutions to second order linear differential equations near ordinary points. It provides an example of finding the series solution to the differential equation y'' + y = 0 near x0 = 0. The solution is found to be a cosine series which represents the cosine function, a fundamental solution. A second example finds the series solution to Airy's equation near x0 = 0, obtaining fundamental solutions related to Airy functions.
Numerical solution of ordinary differential equations GTU CVNM PPT
A ppt on Numerical solution of ordinary differential equations. this PPT contains all gtu content and ideal for gtu students.
Ch07 6
The document discusses complex eigenvalues and eigenvectors for systems of linear differential equations. It shows that if the matrix A has complex conjugate eigenvalue pairs r1 and r2, then the corresponding eigenvectors and solutions will also be complex conjugates. This leads to real-valued fundamental solutions that can express the general solution. An example demonstrates these concepts, finding the complex eigenvalues and eigenvectors and expressing the general solution in terms of real-valued functions. Spiral points, centers, eigenvalues, and trajectory behaviors are also summarized.
Ch05 7
This document discusses series solutions near regular singular points of differential equations. It begins by deriving the recurrence relation for the series coefficients from substituting a power series solution into the differential equation. It then shows how to obtain the indicial equation and exponents at the singular point. Two series solutions are given corresponding to the two exponents. An example problem finds the singular points, exponents, and series solutions for a given third order differential equation.
presentation on Euler and Modified Euler method ,and Fitting of curve
presentation on Euler and Modified Euler method with working and example ,and Fitting of Nonlinear curve using Method of least square
The method of frobenius
The document discusses the Method of Frobenius for solving ordinary differential equations (ODEs) with singular points. It states that the solution for such an ODE is given as an infinite series involving powers of x. To determine the coefficients in the series, one substitutes the series solution into the original ODE, equates coefficients of like powers of x, and obtains the indical equation. Solving this indical equation gives the indicial solution and recurrence relations for the coefficients.
Ch07 8
The document discusses repeated eigenvalues in systems of linear differential equations. If some eigenvalues are repeated, there may not be n linearly independent solutions of the form x = ξert. Additional solutions must be sought that are products of polynomials and exponential functions. For a double eigenvalue r, the first solution is x(1) = ξert, where ξ satisfies (A-rI)ξ = 0. The second solution has the form x(2) = ξtert + ηert, where η satisfies (A-rI)η = ξ and η is called a generalized eigenvector.
Es272 ch7
This document summarizes numerical methods for solving ordinary differential equations (ODEs), including Runge-Kutta methods like Euler's method, Heun's method, and the midpoint method. It also discusses solving systems of ODEs using Euler's method by applying it separately to each equation at each time step. The document provides examples applying these methods to solve sample ODEs and systems of ODEs.
Ch02 7
This document discusses Euler's method for numerically approximating solutions to first-order initial value problems. It begins by introducing Euler's method and its use of tangent lines to approximate the solution curve. Examples are provided to illustrate the application of the method and analyze errors compared to exact solutions. The discussion notes that Euler's method relies on a sequence of tangent lines to different solution curves, so accuracy depends on whether the family of solutions is converging or diverging. It emphasizes the importance of error bounds when exact solutions are unknown.
Introduction to Differential Equations
This document provides an introduction to differential equations. It defines a differential equation as an equation containing an unknown function and its derivatives. Ordinary differential equations are presented, along with definitions of the order and degree of a differential equation. Methods for solving differential equations are introduced, including Taylor series methods, Euler's method, and error analysis. Examples are provided to demonstrate applying these methods.
Lesson 13: Rank and Solutions to Systems of Linear Equations
This document provides an overview of lesson 12 on rank and solutions to systems of linear equations. It defines rank as the maximum number of linearly independent column vectors in a matrix and discusses how to compute rank using Gaussian elimination and minors. It also relates rank to the consistency and redundancy of systems of linear equations, noting that a system is consistent if the rank of the coefficient matrix equals the rank of the augmented matrix, and redundant or free variables exist if the ranks are less than the number of equations or variables respectively.
Properties of bivariate and conditional Gaussian PDFs
Properties of bi-variate Gaussian pdf
Properties of conditional Gaussian pdf
Effect of correlation on bi-variate and conditional Gaussian pdf
Analytic expressions of bivariate and conditional Gaussian pdfs
3-D and 2-D contour plots of Gaussian pdfs
Conditional mean and variance
Matlab code of density functions plots
Advance engineering mathematics
This document discusses methods for solving first order non-linear partial differential equations. It defines ordinary and partial differential equations, and describes four standard forms for first order partial differential equations: 1) equations not involving independent variables, 2) equations reducible to standard form through change of variables, 3) separable equations, and 4) Clairaut's form where the equation can be written as z = px + qy + f(p,q). Examples are provided for each method. Partial differential equations have applications in fields like fluid mechanics, heat transfer, and electromagnetism. The main applications discussed are the heat, wave, and Laplace equations.
Higher order differential equation
This document provides an overview of techniques for solving advanced engineering mathematics problems involving higher order differential equations. It introduces key concepts like auxiliary equations, complementary functions, particular integrals, and methods for solving linear differential equations with constant and variable coefficients. These include the general method, shortcut method, method of undetermined coefficients, and method of variation parameters (Wronskian method). Examples of applying these techniques to solve specific differential equations are also provided.
Calculus ebook
1. The document discusses differentiation rules including the product rule, quotient rule, chain rule, and implicit differentiation. Examples are provided to illustrate how to use each rule to take derivatives.
2. Trigonometric differentiation rules are also covered, including that the derivative of sine is cosine and the derivative of cosine is the negative of sine. Exponential and logarithmic differentiation formulas are defined.
3. The document also discusses parametric differentiation and provides examples of taking derivatives of parametric equations.
Numarical values highlighted
This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Ch07 7
The document discusses fundamental matrices and their properties. A fundamental matrix Ψ(t) is a matrix whose columns are fundamental solutions to the system x' = P(t)x. Ψ(t) satisfies the differential equation Ψ' = P(t)Ψ and is nonsingular. The general solution to the system can be written as x = Ψ(t)c, where c is a constant vector. For an initial value problem, the solution is x = Ψ(t)Ψ-1(t0)x0. The fundamental matrix Φ(t) corresponding to a set of fundamental solutions satisfying initial conditions is also discussed. Matrix exponential functions are introduced as the fundamental matrix
Higher Order Differential Equation
The document provides an overview of advanced engineering mathematics concepts for differential equations. It covers topics such as homogeneous and non-homogeneous linear differential equations with constant and variable coefficients. Methods for solving differential equations are discussed, including finding the auxiliary equation, complementary function, and particular integral. Specific solving techniques like the Cauchy-Euler and Legendre methods for variable coefficient equations are also mentioned. Examples of different types of differential equations are provided throughout.
Unit1 vrs
The document discusses numerical methods for solving ordinary differential equations (ODEs), including Taylor's series method and Picard's method. It provides examples of applying Taylor's series method to approximate solutions of first order ODEs at different values of x to 4-5 decimal places of accuracy. The examples given include solving ODEs with initial conditions and computing solutions at multiple x values by taking terms from the Taylor series expansion.
Numarical values
This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Ch6 series solutions algebra
The document provides an overview of power series methods for solving differential equations. It defines key concepts like radius of convergence, region of convergence, and ordinary points. It also outlines the basic steps of the power series method: (1) assume a power series solution; (2) derive the recurrence relation; (3) determine the coefficients to obtain particular solutions. Examples are provided to illustrate these steps in finding series solutions to ordinary differential equations about ordinary points.
masters-presentation
This document describes Chebyshev polynomials and their use in spectral methods. It discusses:
- Using Lagrange interpolation over Chebyshev points to get near-best polynomial approximations.
- Representing functions on [-1,1] as Chebyshev polynomial expansions for fast computations.
- Defining a "Chebfun" as a minimal-degree interpolant using this representation.
- Algorithms for differentiating, integrating, and finding roots of Chebfuns efficiently in Python.
- Future work on using Chebfuns to solve differential equations spectrally.
Ch05 6
This document discusses solving second-order linear differential equations near a regular singular point, which is done by assuming power series solutions and obtaining recursion relations between the coefficients. Specifically, it provides an example of solving the differential equation ( ) 012 2=++′−′′ yxyxyx near the regular singular point x=0. Two linearly independent solutions are obtained in the forms of ( )( )∑∞=1!12753)1( nnnxaxy and ( )( )∑∞=12/1!12531)1( nnnxaxy , yielding the general solution ( )0),()()( 2211 >+= xxycxycxy .
More Related Content
What's hot
Numerical solution of ordinary differential equations GTU CVNM PPT
A ppt on Numerical solution of ordinary differential equations. this PPT contains all gtu content and ideal for gtu students.
Ch07 6
The document discusses complex eigenvalues and eigenvectors for systems of linear differential equations. It shows that if the matrix A has complex conjugate eigenvalue pairs r1 and r2, then the corresponding eigenvectors and solutions will also be complex conjugates. This leads to real-valued fundamental solutions that can express the general solution. An example demonstrates these concepts, finding the complex eigenvalues and eigenvectors and expressing the general solution in terms of real-valued functions. Spiral points, centers, eigenvalues, and trajectory behaviors are also summarized.
Ch05 7
This document discusses series solutions near regular singular points of differential equations. It begins by deriving the recurrence relation for the series coefficients from substituting a power series solution into the differential equation. It then shows how to obtain the indicial equation and exponents at the singular point. Two series solutions are given corresponding to the two exponents. An example problem finds the singular points, exponents, and series solutions for a given third order differential equation.
presentation on Euler and Modified Euler method ,and Fitting of curve
presentation on Euler and Modified Euler method with working and example ,and Fitting of Nonlinear curve using Method of least square
The method of frobenius
The document discusses the Method of Frobenius for solving ordinary differential equations (ODEs) with singular points. It states that the solution for such an ODE is given as an infinite series involving powers of x. To determine the coefficients in the series, one substitutes the series solution into the original ODE, equates coefficients of like powers of x, and obtains the indical equation. Solving this indical equation gives the indicial solution and recurrence relations for the coefficients.
Ch07 8
The document discusses repeated eigenvalues in systems of linear differential equations. If some eigenvalues are repeated, there may not be n linearly independent solutions of the form x = ξert. Additional solutions must be sought that are products of polynomials and exponential functions. For a double eigenvalue r, the first solution is x(1) = ξert, where ξ satisfies (A-rI)ξ = 0. The second solution has the form x(2) = ξtert + ηert, where η satisfies (A-rI)η = ξ and η is called a generalized eigenvector.
Es272 ch7
This document summarizes numerical methods for solving ordinary differential equations (ODEs), including Runge-Kutta methods like Euler's method, Heun's method, and the midpoint method. It also discusses solving systems of ODEs using Euler's method by applying it separately to each equation at each time step. The document provides examples applying these methods to solve sample ODEs and systems of ODEs.
Ch02 7
This document discusses Euler's method for numerically approximating solutions to first-order initial value problems. It begins by introducing Euler's method and its use of tangent lines to approximate the solution curve. Examples are provided to illustrate the application of the method and analyze errors compared to exact solutions. The discussion notes that Euler's method relies on a sequence of tangent lines to different solution curves, so accuracy depends on whether the family of solutions is converging or diverging. It emphasizes the importance of error bounds when exact solutions are unknown.
Introduction to Differential Equations
This document provides an introduction to differential equations. It defines a differential equation as an equation containing an unknown function and its derivatives. Ordinary differential equations are presented, along with definitions of the order and degree of a differential equation. Methods for solving differential equations are introduced, including Taylor series methods, Euler's method, and error analysis. Examples are provided to demonstrate applying these methods.
Lesson 13: Rank and Solutions to Systems of Linear Equations
This document provides an overview of lesson 12 on rank and solutions to systems of linear equations. It defines rank as the maximum number of linearly independent column vectors in a matrix and discusses how to compute rank using Gaussian elimination and minors. It also relates rank to the consistency and redundancy of systems of linear equations, noting that a system is consistent if the rank of the coefficient matrix equals the rank of the augmented matrix, and redundant or free variables exist if the ranks are less than the number of equations or variables respectively.
Properties of bivariate and conditional Gaussian PDFs
Properties of bi-variate Gaussian pdf
Properties of conditional Gaussian pdf
Effect of correlation on bi-variate and conditional Gaussian pdf
Analytic expressions of bivariate and conditional Gaussian pdfs
3-D and 2-D contour plots of Gaussian pdfs
Conditional mean and variance
Matlab code of density functions plots
Advance engineering mathematics
This document discusses methods for solving first order non-linear partial differential equations. It defines ordinary and partial differential equations, and describes four standard forms for first order partial differential equations: 1) equations not involving independent variables, 2) equations reducible to standard form through change of variables, 3) separable equations, and 4) Clairaut's form where the equation can be written as z = px + qy + f(p,q). Examples are provided for each method. Partial differential equations have applications in fields like fluid mechanics, heat transfer, and electromagnetism. The main applications discussed are the heat, wave, and Laplace equations.
Higher order differential equation
This document provides an overview of techniques for solving advanced engineering mathematics problems involving higher order differential equations. It introduces key concepts like auxiliary equations, complementary functions, particular integrals, and methods for solving linear differential equations with constant and variable coefficients. These include the general method, shortcut method, method of undetermined coefficients, and method of variation parameters (Wronskian method). Examples of applying these techniques to solve specific differential equations are also provided.
Calculus ebook
1. The document discusses differentiation rules including the product rule, quotient rule, chain rule, and implicit differentiation. Examples are provided to illustrate how to use each rule to take derivatives.
2. Trigonometric differentiation rules are also covered, including that the derivative of sine is cosine and the derivative of cosine is the negative of sine. Exponential and logarithmic differentiation formulas are defined.
3. The document also discusses parametric differentiation and provides examples of taking derivatives of parametric equations.
Numarical values highlighted
This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Ch07 7
The document discusses fundamental matrices and their properties. A fundamental matrix Ψ(t) is a matrix whose columns are fundamental solutions to the system x' = P(t)x. Ψ(t) satisfies the differential equation Ψ' = P(t)Ψ and is nonsingular. The general solution to the system can be written as x = Ψ(t)c, where c is a constant vector. For an initial value problem, the solution is x = Ψ(t)Ψ-1(t0)x0. The fundamental matrix Φ(t) corresponding to a set of fundamental solutions satisfying initial conditions is also discussed. Matrix exponential functions are introduced as the fundamental matrix
Higher Order Differential Equation
The document provides an overview of advanced engineering mathematics concepts for differential equations. It covers topics such as homogeneous and non-homogeneous linear differential equations with constant and variable coefficients. Methods for solving differential equations are discussed, including finding the auxiliary equation, complementary function, and particular integral. Specific solving techniques like the Cauchy-Euler and Legendre methods for variable coefficient equations are also mentioned. Examples of different types of differential equations are provided throughout.
Unit1 vrs
The document discusses numerical methods for solving ordinary differential equations (ODEs), including Taylor's series method and Picard's method. It provides examples of applying Taylor's series method to approximate solutions of first order ODEs at different values of x to 4-5 decimal places of accuracy. The examples given include solving ODEs with initial conditions and computing solutions at multiple x values by taking terms from the Taylor series expansion.
Numarical values
This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Ch6 series solutions algebra
The document provides an overview of power series methods for solving differential equations. It defines key concepts like radius of convergence, region of convergence, and ordinary points. It also outlines the basic steps of the power series method: (1) assume a power series solution; (2) derive the recurrence relation; (3) determine the coefficients to obtain particular solutions. Examples are provided to illustrate these steps in finding series solutions to ordinary differential equations about ordinary points.
What's hot (20)
Numerical solution of ordinary differential equations GTU CVNM PPT
Numerical solution of ordinary differential equations GTU CVNM PPT
presentation on Euler and Modified Euler method ,and Fitting of curve
presentation on Euler and Modified Euler method ,and Fitting of curve
Lesson 13: Rank and Solutions to Systems of Linear Equations
Lesson 13: Rank and Solutions to Systems of Linear Equations
Properties of bivariate and conditional Gaussian PDFs
Properties of bivariate and conditional Gaussian PDFs
Viewers also liked
masters-presentation
This document describes Chebyshev polynomials and their use in spectral methods. It discusses:
- Using Lagrange interpolation over Chebyshev points to get near-best polynomial approximations.
- Representing functions on [-1,1] as Chebyshev polynomial expansions for fast computations.
- Defining a "Chebfun" as a minimal-degree interpolant using this representation.
- Algorithms for differentiating, integrating, and finding roots of Chebfuns efficiently in Python.
- Future work on using Chebfuns to solve differential equations spectrally.
Ch05 6
This document discusses solving second-order linear differential equations near a regular singular point, which is done by assuming power series solutions and obtaining recursion relations between the coefficients. Specifically, it provides an example of solving the differential equation ( ) 012 2=++′−′′ yxyxyx near the regular singular point x=0. Two linearly independent solutions are obtained in the forms of ( )( )∑∞=1!12753)1( nnnxaxy and ( )( )∑∞=12/1!12531)1( nnnxaxy , yielding the general solution ( )0),()()( 2211 >+= xxycxycxy .
Observación de una clase
Observación de una clase dirigida por el maestro titular del grupo en que realicé mi tercer jornada de observación y mi práctica docente.
Financial Aid
This document provides information about applying for financial aid. It explains that students should complete the Free Application for Federal Student Aid (FAFSA) each year as close to January 1st as possible to be considered for federal and state grants, loans, work-study and scholarships. Even those who think their family income is too high should still apply. The FAFSA takes into account taxes, income, family size and other factors to calculate the expected family contribution. The document outlines the application process and required information including tax documents and social security numbers. It also describes different types of federal and state aid available as well as scholarships, loans and payment plans.
สารสนเทศเพื่อประกอบการตัดสินใจ
1 นายสมิต จิตรบวรวงศ์ เลขที่1
2 นายคณาพงศ์ นิยม เลขที่2
3 นายธนกฤต วัฒถาพร เลขที่3
4 นายบารมี ชมพู่ เลขที่5
5 นายพีรณัฐ อุณหะนันทน์ เลขที่10
6 นายก้องภพ สุขแสงเดือนฉาย เลขที่11
7 นางสาวจิรวัส แสงนิ่ม เลขที่13
8 นางสาวพรรนิภา แซ่ตัน เลขที่17
ชั้นมัธยมศึกษาปีที่5/2
Isomorphism
This document discusses isomorphism, one-to-one and onto linear transformations, and provides examples. It defines isomorphism as when two vector spaces are said to be isomorphic if there exists a linear transformation between them that is both one-to-one and onto. It provides theorems relating the dimension of isomorphic spaces and characterizations of one-to-one and onto linear transformations in terms of the kernel, rank, and nullity. Examples are given to determine whether linear transformations are one-to-one and/or onto based on their rank and nullity. Finally, several vector spaces are stated to be isomorphic to each other.
From Finish to Start
This document provides an agenda and information for a professional development session on instructional planning for science teachers. The session goals are to identify key science standards assessed on state tests, analyze test questions to determine required skills, and learn how to incorporate the 5E instructional model into lesson planning. The agenda includes identifying important "heavy hitter" standards, deconstructing sample test questions, and using a template to design a 5E lesson plan focusing on a standard. Contact information is also provided for instructional support staff.
Legendre functions
The document discusses Legendre functions, which are solutions to Legendre's differential equation. Legendre functions arise when solving Laplace's equation in spherical coordinates. Legendre polynomials were first introduced by Adrien-Marie Legendre in 1785 as coefficients in an expansion of Newtonian potential. The document covers topics such as Legendre polynomials, Rodrigues' formula, orthogonality of Legendre polynomials, and associated Legendre functions.
FIWARE: Managing Context Information at Large Scale (NGSIv1)
This document provides an introduction and overview of the Orion Context Broker for managing context information at large scale. It discusses how Orion implements the OMA NGSI standard API for creating, retrieving, updating, and subscribing to context entities and their attributes. It provides examples of basic operations like creating entities and attributes, updating their values, and querying for information. It also demonstrates more advanced operations like subscriptions and notifications. Overall, the document serves as a tutorial for getting started with the main functions and capabilities of the Orion Context Broker.
Ch05 5
The document discusses solutions to Euler equations, which are differential equations of the form 0][ 2=+′+′′= yyxyxyL βα. It provides the general solutions based on whether the roots r1 and r2 of the characteristic equation are real/distinct, equal, or complex. For initial value problems, the constants in the general solution are determined using the given initial conditions. Near the singular point x=0, the qualitative behavior of the solutions depends on the nature of the roots r1 and r2.
Ch03 1
The document discusses solving second order linear homogeneous differential equations with constant coefficients. It explains that the characteristic equation is obtained by substituting an exponential solution into the differential equation. The roots of the characteristic equation determine the general solution, which is a linear combination of exponential terms. Initial value problems can then be solved for the coefficients by applying the initial conditions to the general solution. Several examples illustrate these steps to solve initial value problems for different differential equations.
Curso AngularJS - 3. módulos y controladores
Curso AngularJS.
Temas:
1. Introducción
2. Conceptos básicos
3. Módulos y controladores
4. Filtros y servicios
5. Rutas
6. Formularios
7. Temas avanzados
Linear differential equation with constant coefficient
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
Ordinary differential equations
The document is an introduction to ordinary differential equations prepared by Ahmed Haider Ahmed. It defines key terms like differential equation, ordinary differential equation, partial differential equation, order, degree, and particular and general solutions. It then provides methods for solving various types of first order differential equations, including separable, homogeneous, exact, linear, and Bernoulli equations. Specific examples are given to illustrate each method.
Higher Differential Equation
1) Ordinary differential equations relate a dependent variable to one or more independent variables by means of differential coefficients. They can be classified based on order, degree, whether they are linear or non-linear, and type (exact, separable variables, homogeneous).
2) First order differential equations can sometimes be solved by separation of variables, or by finding an integrating factor. Homogeneous equations can be transformed by substitution.
3) Second order linear differential equations can be reduced to a system of two first order equations. The complementary function and particular solutions combine to form the general solution. Unequal or equal roots of the characteristic equation determine the form of the complementary function.
3 torsion- Mechanics of Materials - 4th - Beer
This document provides an overview of chapter 3 from the textbook "Mechanics of Materials" which covers the topic of torsion. It begins with an introduction to torsional loads on circular shafts and the concept of net torque due to internal stresses. Key concepts discussed include shear strain, stresses in the elastic range using elastic torsion formulas, and failure modes under torsion. The document provides examples of solving sample problems involving statically indeterminate shafts, determining required shaft diameters, and calculating stresses and angles of twist. It concludes with discussing plastic deformations and torsion of noncircular members.
Viewers also liked (20)
FIWARE: Managing Context Information at Large Scale (NGSIv1)
FIWARE: Managing Context Information at Large Scale (NGSIv1)
Linear differential equation with constant coefficient
Linear differential equation with constant coefficient
Similar to Classification of singularity
Analytic Function of Power Series
In this ppt i gave information regarding....
> Analytic function
> ordinary point &
> singular point with proper flow chart and example
Numerical Methods.pptx
This document discusses numerical methods for interpolation and solving algebraic and transcendental equations. It provides examples of using Newton's forward and backward interpolation formulas to find function values between given data points. Lagrange's interpolation formula is also introduced as a way to find function values using all the given data points, whether they are equally spaced or not. Three examples are worked through applying these interpolation methods to find unknown function values from tables of x and y data pairs.
NPDE-TCA
This document presents an internship project report on multistep methods for solving initial value problems of ordinary differential equations. It introduces the basic problem of finding the function y(t) that satisfies a given differential equation and initial condition. It discusses existence and uniqueness theorems, Picard's method of successive approximations, and approaches for approximating the required integrations, including the derivative, Taylor series, and Euler's methods. The report appears to evaluate various one-step and multistep numerical methods for solving initial value problems, including Runge-Kutta, Adams-Bashforth, and Adams-Moulton methods.
lec36.ppt
The document summarizes key results from complex analysis including:
Cauchy's integral theorem which states that if f(z) is analytic in a simply connected region, the integral around any closed curve in that region is zero.
Morera's theorem, the converse of Cauchy's theorem, which states that if the integral is zero around every closed curve, then the function is analytic.
Cauchy's integral formula which expresses the value of an analytic function at a point inside a contour as a contour integral.
The generalization of Cauchy's integral formula for functions with poles inside the contour.
DIFFERENTAL CALCULUS DERIVATIVES FIRST PART
The document defines derivatives and differentiation rules. It provides definitions for the tangent line, normal line, and derivative of a function. Notation for derivatives is explained. Common differentiation rules are stated, including the power rule, product rule, quotient rule, and differentiation formulas for trigonometric, inverse trigonometric, exponential, logarithmic, hyperbolic and inverse hyperbolic functions. Examples of computing derivatives are worked out applying these rules.
WEEK 1 QUADRATIC EQUATION.pptx
A quadratic equation is any equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. It is an equation of the second degree that contains at least one term that is squared. The ax^2 term is called the quadratic term, the bx term is the linear term, and c is the constant term. There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula.
BSC_COMPUTER _SCIENCE_UNIT-2_DISCRETE MATHEMATICS
This document provides an introduction to definite integration and its applications. It defines indefinite integration as finding the integral or primitive function F(x) of a function f(x). Definite integration involves finding the area under a curve defined by a function f(x) over a specified interval. Standard formulae for integrating common functions like polynomials, trigonometric functions, and exponentials are provided. Methods for integrating functions using substitution and integration by parts are described. Examples of applying these techniques to evaluate definite integrals are also given.
Study Material Numerical Solution of Odinary Differential Equations
1. The document provides information about a numerical methods course for physics majors at Vivekananda College in Tiruvedakam West, including the reference textbook and details about Unit V on numerical solutions of ordinary differential equations.
2. It introduces the concept of using Taylor series approximations to find numerical solutions to differential equations, providing the general Taylor series expansion formula and explaining how to derive the terms needed to solve specific differential equations.
3. It gives examples of using the Taylor series method to solve sample ordinary differential equations, finding approximate values of y at increasing values of x to several decimal places.
lec38.ppt
1) Jordan's lemma is used to convert real integrals over the infinite real axis into complex integrals over a contour enclosing the real axis in the complex plane.
2) Several examples are provided of using residues and Jordan's lemma to evaluate definite integrals over the real line or infinite intervals that involve functions with poles, including integrals of x^2, sin(x)/x, 1/(x^2+a^2)^2, and sin(x)/(x(x^2+a^2)).
3) The technique involves closing the contour with a semicircle at infinity where the integral over the semicircle goes to zero by Jordan's lemma, leaving the original integral equal to the residue theorem applied to the
Trapezoidal Method IN Numerical Analysis
The document defines the trapezoidal rule for approximating definite integrals. It provides the trapezoidal formula, explains the geometric interpretation of dividing the region into trapezoids, and outlines an algorithm and flowchart for implementing the trapezoidal rule in Python. Sample problems applying the trapezoidal rule are included to evaluate definite integrals numerically.
FOURIER SERIES Presentation of given functions.pptx
This document discusses periodic functions and their Fourier series representations. It defines periodic functions as those where f(x+T)=f(x) for some period T. Examples given are sin(x), cos(x), and tan(x) with periods of 2π, 2π, and π respectively. It also defines piecewise continuous functions and gives Dirichlet's conditions for the existence of a Fourier series representation over an interval. Specific examples are worked out, including finding the Fourier series of |sin(x)| from -π to π and a piecewise defined function from -π to π. The document derives results for Fourier series over various intervals.
The derivatives module03
The document defines the tangent line and derivative of a function. It provides examples of finding the slope of the tangent line and derivative for various functions at given points using limits. Specifically, it shows how to calculate the slope of the tangent line to f(x)=2x^3 - 1 at (2,15), finding the equation of the tangent line to f(x)=x^2 at (1,1), and calculating the derivative of f(x)=x^2.
Power Series - Legendre Polynomial - Bessel's Equation
The presentation shows types of equations inside every topic along with its general form, generating formula, and other equations like recursion, frobenius, rodrigues etc for calculus. Its an overall explanation in a brief. You are at correct link to get your work done out of this in your engineering maths.
Functions of severable variables
Partial differentiation, total differentiation, Jacobian, Taylor's expansion, stationary points,maxima & minima (Extreme values),constraint maxima & minima ( Lagrangian multiplier), differentiation of implicit functions.
doc
This document is an internship project report submitted by Siddharth Pujari to the Indian Institute of Space Science and Technology. The report focuses on advanced control system design for aircraft and simulating aircraft trajectory. It includes modeling an aircraft's state space model in MATLAB to test controllability. The report also covers theoretical aspects of stability of linear systems, linearizing nonlinear models, controllability of linear systems using the Kalman criterion and transition matrix, and applying these concepts to simulate aircraft controllability in MATLAB.
Fourier series
Periodic Function, Dirichlet's Condition, Fourier series, Even & Odd functions, Euler's Formula for Fourier Coefficients, Change of Interval, Fourier series in the intervals (0,2l), (-l,l) , (-pi, pi), (0, 2pi), Half Range Cosine & Sine series Root mean square, Complex Form of Fourier series, Parseval's Identity
Existence, Uniqueness and Stability Solution of Differential Equations with B...
In this work, we investigate the existence ,uniqueness and stability solution of non-linear
differential equations with boundary conditions by using both method Picard approximation and
Banach fixed point theorem which were introduced by [6] .These investigations lead us to improving
and extending the above method. Also we expand the results obtained by [1] to change the non-linear
differential equations with initial condition to non-linear differential equations with boundary
conditions
sistem non linier Lyapunov Stability
Lyapunov stability is named after Aleksandr Lyapunov and considers stability in nonlinear systems. There are two main definitions of Lyapunov stability: 1) an equilibrium point is stable if solutions starting near it remain near it, and 2) an equilibrium point is stable if the operator mapping initial to solution values is continuous at that point. Asymptotic stability further requires that solutions converge over time. Lyapunov sought conditions ensuring stability rather than just boundedness or convergence alone.
26 Computational Geometry
Here is a description of the classic computer graphic algorithms. Examples of those problems are:
1- Line segment intersection
2.- Convex Hull
Ordinary Differential Equations: Variable separation method
First order and first degree differential equations, Variable separation method ,17 solved problems with detailed simplification
Similar to Classification of singularity (20)
Study Material Numerical Solution of Odinary Differential Equations
Study Material Numerical Solution of Odinary Differential Equations
FOURIER SERIES Presentation of given functions.pptx
FOURIER SERIES Presentation of given functions.pptx
Power Series - Legendre Polynomial - Bessel's Equation
Power Series - Legendre Polynomial - Bessel's Equation
Existence, Uniqueness and Stability Solution of Differential Equations with B...
Existence, Uniqueness and Stability Solution of Differential Equations with B...
Ordinary Differential Equations: Variable separation method
Ordinary Differential Equations: Variable separation method
More from Raj Parekh
Intrenet and its uses
The document provides an overview of the Internet and how it works:
- The Internet is a global network that allows computers to share information electronically. It can be accessed from anywhere through an Internet connection.
- Web pages are identified by URLs and displayed in web browsers like Safari, Internet Explorer, Google Chrome, and Mozilla Firefox. A URL includes the protocol, server, path, and resource name.
- The Internet has grown from ARPANET in the 1960s and key developments like the introduction of email, the World Wide Web, and graphical web browsers. It enables access to information through various services like web pages, email, file transfers, messaging, and voice calls.
Fuel cells and its types
The document discusses fuel cells, including:
1) A fuel cell generates electricity through an electrochemical reaction between a fuel (typically hydrogen) and oxygen, with water and heat as byproducts.
2) Fuel cells have several types but all consist of an anode, cathode, and electrolyte; they operate by separating the fuel from the oxygen to prevent combustion.
3) Applications include stationary power systems, transportation such as fuel cell vehicles and buses, and portable power devices, with each fuel cell type suited to certain uses.
Switch statement, break statement, go to statement
The document discusses various control flow statements in C programming including switch case statement, break statement, and goto statement. It provides the syntax and meaning of switch case statement which allows executing different code blocks based on the value of an expression. It also explains the break statement which terminates the execution of a switch case or loop statement. The goto statement allows transferring program control unconditionally to another label in the program.
3 d-printing
This document discusses the intellectual property implications of 3D printing. It summarizes that under UK law, design rights, patents, and trademarks are not infringed by personal or non-commercial use of 3D printers. Copyright protection also does not typically apply to most 3D objects that could be reproduced. While control of IP may become problematic as 3D printing technologies improve and designs/files are more openly shared, currently disseminating design files does not clearly infringe upon patents or copyrights in those files under UK law. The document provides an overview of the relevant IP laws and concludes that the legal outlook suggests private and non-commercial 3D printing will not usually infringe upon intellectual property rights.
Linear transformation.ppt
This document discusses linear transformations and their properties. It defines a linear transformation as a function between vector spaces that preserves vector addition and scalar multiplication. The kernel of a linear transformation is the set of vectors mapped to the zero vector, and is a subspace of the domain. The range is the set of images of all vectors under the transformation. Matrices can represent linear transformations, with the matrix equation representing the transformation of vectors. Examples are provided to illustrate key concepts such as kernels, ranges, and matrix representations of linear transformations.
Rain water harvesting
Rainwater harvesting involves collecting, conveying, and storing rainwater for beneficial use. It can provide a reliable source of water as rainfall averages around 4 million liters annually per acre that can be collected. As rainwater harvesting is neither energy-intensive nor labor-intensive, it serves as a cost-effective water solution. Various methodologies for rainwater harvesting include collecting from roofs, land, and entire watersheds. The advantages are that it provides self-sufficiency to water supply, reduces pumping costs, offers high-quality soft water, improves groundwater quality, and reduces soil erosion and flooding in urban areas.
Cs
This document discusses various aspects of communication skills, with a focus on pronunciation and voice modulation. It provides tips for proper pronunciation, the importance of pronunciation in communication. It also discusses voice modulation techniques like volume, pitch, pace, emphasis and inflection. The document emphasizes using pauses to allow listeners to absorb information and to replace filler words. Pauses also help speakers organize their thoughts and allow their mind to "catch up" to their speech. Proper pronunciation, modulation, and use of pauses are important for clear communication.
Msm
Solidification is the process where a liquid turns into a solid when its temperature is lowered below the freezing point. Nucleation is the first step of solidification, where tiny stable nuclei are created in the liquid metal. There are two types of nucleation: homogeneous nucleation which occurs from clustering of atoms at high undercooling, and heterogeneous nucleation which occurs more commonly on surfaces like the mold walls or impurities. Once a nucleus reaches the critical size, growth will occur as more atoms attach in an exothermic process releasing heat, which must be removed for solidification to continue. Understanding nucleation and solidification is important for industrial casting and welding processes where metal melting and resolidification occurs.
Various work holding devices
This document summarizes various types of work holding devices used in lathe machines, including four jaw independent chucks, three jaw universal chucks, combination chucks, magnetic chucks, collet chucks, drill chucks, lathe centers, steady rests, follower rests, mandrels, lathe dogs, and lathe face plates. It provides brief descriptions of each device, highlighting their main features and purposes.
Newton's forward difference
This document provides Newton's formula for forward difference interpolation and an example of using it to find the value of tan(0.12).
- Newton's formula uses forward difference interpolation to find the value of a polynomial of degree n that fits a set of (n+1) equally spaced (x,y) points.
- The coefficients of the polynomial are determined using forward differences of the y-values.
- In the example, the value of tan(0.12) is found by applying Newton's formula to a table of tan(x) values from 0.10 to 0.30 using forward differences up to degree 4.
Metal melting furnaces
The document discusses different types of metal melting furnaces used in metal casting. It describes Cupola Furnaces, Electric Arc Furnaces, Induction Furnaces, and Metal Pot Furnaces. Cupola Furnaces use layers of metal, coke and limestone fed into the top to melt iron and ferrous alloys through combustion. Electric Arc Furnaces use carbon electrodes to generate arcs and melt metal through heat. Induction Furnaces use electromagnetic induction to rapidly heat and melt metals. Metal Pot Furnaces are used for low melting point alloys like aluminum and are heated by gas or oil without direct contact between flames and metal.
More from Raj Parekh (11)
Switch statement, break statement, go to statement
Switch statement, break statement, go to statement
Recently uploaded
一比一原版(psu学位证书)美国匹兹堡州立大学毕业证如何办理
原版一模一样【微信：741003700 】【(psu学位证书)美国匹兹堡州立大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(psu学位证书)美国匹兹堡州立大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(psu学位证书)美国匹兹堡州立大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(psu学位证书)美国匹兹堡州立大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(psu学位证书)美国匹兹堡州立大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
OOPS_Lab_Manual - programs using C++ programming language
This manual contains programs on object oriented programming concepts using C++ language.
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
The Network on Chip (NoC) has emerged as an effective
solution for intercommunication infrastructure within System on
Chip (SoC) designs, overcoming the limitations of traditional
methods that face significant bottlenecks. However, the complexity
of NoC design presents numerous challenges related to
performance metrics such as scalability, latency, power
consumption, and signal integrity. This project addresses the
issues within the router's memory unit and proposes an enhanced
memory structure. To achieve efficient data transfer, FIFO buffers
are implemented in distributed RAM and virtual channels for
FPGA-based NoC. The project introduces advanced FIFO-based
memory units within the NoC router, assessing their performance
in a Bi-directional NoC (Bi-NoC) configuration. The primary
objective is to reduce the router's workload while enhancing the
FIFO internal structure. To further improve data transfer speed,
a Bi-NoC with a self-configurable intercommunication channel is
suggested. Simulation and synthesis results demonstrate
guaranteed throughput, predictable latency, and equitable
network access, showing significant improvement over previous
designs
Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...
Consolidation Settlement Calculation Program-The Python Code
By Professor Dr. Costas Sachpazis, Civil Engineer & Geologist
This program calculates the consolidation settlement for a foundation based on soil layer properties and foundation data. It allows users to input multiple soil layers and foundation characteristics to determine the total settlement.
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
原版一模一样【微信：741003700 】【(爱大毕业证书)爱荷华大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
Call Girls Goa (india) ☎️ +91-7426014248 Goa Call Girl
Call Girls Goa (india) ☎️ +91-7426014248 Goa Call Girl
An In-Depth Exploration of Natural Language Processing: Evolution, Applicatio...
Natural language processing (NLP) has
recently garnered significant interest for the
computational representation and analysis of human
language. Its applications span multiple domains such
as machine translation, email spam detection,
information extraction, summarization, healthcare,
and question answering. This paper first delineates
four phases by examining various levels of NLP and
components of Natural Language Generation,
followed by a review of the history and progression of
NLP. Subsequently, we delve into the current state of
the art by presenting diverse NLP applications,
contemporary trends, and challenges. Finally, we
discuss some available datasets, models, and
evaluation metrics in NLP.
Ericsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques
Determination of Equivalent Circuit parameters and performance characteristic...
Includes the testing of induction motor to draw the circle diagram of induction motor with step wise procedure and calculation for the same. Also explains the working and application of Induction generator
Blood finder application project report (1).pdf
Blood Finder is an emergency time app where a user can search for the blood banks as
well as the registered blood donors around Mumbai. This application also provide an
opportunity for the user of this application to become a registered donor for this user have
to enroll for the donor request from the application itself. If the admin wish to make user
a registered donor, with some of the formalities with the organization it can be done.
Specialization of this application is that the user will not have to register on sign-in for
searching the blood banks and blood donors it can be just done by installing the
application to the mobile.
The purpose of making this application is to save the user’s time for searching blood of
needed blood group during the time of the emergency.
This is an android application developed in Java and XML with the connectivity of
SQLite database. This application will provide most of basic functionality required for an
emergency time application. All the details of Blood banks and Blood donors are stored
in the database i.e. SQLite.
This application allowed the user to get all the information regarding blood banks and
blood donors such as Name, Number, Address, Blood Group, rather than searching it on
the different websites and wasting the precious time. This application is effective and
user friendly.
Sri Guru Hargobind Ji - Bandi Chor Guru.pdf
Sri Guru Hargobind Ji (19 June 1595 - 3 March 1644) is revered as the Sixth Nanak.
• On 25 May 1606 Guru Arjan nominated his son Sri Hargobind Ji as his successor. Shortly
afterwards, Guru Arjan was arrested, tortured and killed by order of the Mogul Emperor
Jahangir.
• Guru Hargobind's succession ceremony took place on 24 June 1606. He was barely
eleven years old when he became 6th Guru.
• As ordered by Guru Arjan Dev Ji, he put on two swords, one indicated his spiritual
authority (PIRI) and the other, his temporal authority (MIRI). He thus for the first time
initiated military tradition in the Sikh faith to resist religious persecution, protect
people’s freedom and independence to practice religion by choice. He transformed
Sikhs to be Saints and Soldier.
• He had a long tenure as Guru, lasting 37 years, 9 months and 3 days
一比一原版(USF毕业证)旧金山大学毕业证如何办理
原件一模一样【微信：95270640】【旧金山大学毕业证USF学位证成绩单】【微信：95270640】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：95270640】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：95270640】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份【微信：95270640】
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
办理旧金山大学毕业证毕业证学位证USF学位证【微信：95270640 】外观非常精致，由特殊纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理旧金山大学毕业证USF学位证毕业证学位证【微信：95270640 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理旧金山大学毕业证毕业证学位证USF学位证【微信：95270640 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理旧金山大学毕业证毕业证学位证USF学位证【微信：95270640 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
Impartiality as per ISO /IEC 17025:2017 Standard
This document provides basic guidelines for imparitallity requirement of ISO 17025. It defines in detial how it is met and wiudhwdih jdhsjdhwudjwkdbjwkdddddddddddkkkkkkkkkkkkkkkkkkkkkkkwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwioiiiiiiiiiiiii uwwwwwwwwwwwwwwwwhe wiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq gbbbbbbbbbbbbb owdjjjjjjjjjjjjjjjjjjjj widhi owqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq uwdhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhwqiiiiiiiiiiiiiiiiiiiiiiiiiiiiw0pooooojjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj whhhhhhhhhhh wheeeeeeee wihieiiiiii wihe
e qqqqqqqqqqeuwiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiqw dddddddddd cccccccccccccccv s w c r
cdf cb bicbsad ishd d qwkbdwiur e wetwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w
dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffw
uuuuhhhhhhhhhhhhhhhhhhhhhhhhe qiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ccccccccccccccccccccccccccccccccccc bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuum
m
m mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm m i
g i dijsd sjdnsjd ndjajsdnnsa adjdnawddddddddddddd uw
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
3rd International Conference on Artificial Intelligence Advances (AIAD 2024) will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the area advanced Artificial Intelligence. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and advancement in the research area. Core areas of AI and advanced multi-disciplinary and its applications will be covered during the conferences.
FULL STACK PROGRAMMING - Both Front End and Back End
This ppt gives details about Full Stack Programming and its basics.
Recently uploaded (20)
OOPS_Lab_Manual - programs using C++ programming language
OOPS_Lab_Manual - programs using C++ programming language
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...
Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...
Call Girls Goa (india) ☎️ +91-7426014248 Goa Call Girl
Call Girls Goa (india) ☎️ +91-7426014248 Goa Call Girl
An In-Depth Exploration of Natural Language Processing: Evolution, Applicatio...
An In-Depth Exploration of Natural Language Processing: Evolution, Applicatio...
Ericsson LTE Throughput Troubleshooting Techniques.ppt
Ericsson LTE Throughput Troubleshooting Techniques.ppt
Determination of Equivalent Circuit parameters and performance characteristic...
Determination of Equivalent Circuit parameters and performance characteristic...
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
FULL STACK PROGRAMMING - Both Front End and Back End
FULL STACK PROGRAMMING - Both Front End and Back End
Classification of singularity
- 1. POWER SERIES & CLASSIFICATION OF SINGULARITY NAME: RAJ PAREKH ENROLLMENT NO: 140990119029 SUBJECT: AEM
- 2. Introduction To Power Series A power series of (x – x0) is an infinite series of the form : If a = 0 then Consider Second Order Linear Homogeneous Differential Equation Then, 𝑑2 𝑦 𝑑𝑥2 + 𝑃 𝑥 𝑑𝑦 𝑑𝑥 + 𝑄 𝑥 𝑦 = 0 Where 𝑃 𝑥 = 𝑃1(𝑥) 𝑃0(𝑥) & 𝑄 𝑥 = 𝑃2(𝑥) 𝑃0(𝑥) 𝑘=0 ∞ 𝜒 − 𝜒0 𝑘 𝑎0 + 𝑎1(𝑥 − 𝑥0) + 𝑎2 𝑥 − 𝑥0 2 +. . . . . . . . . +𝑎 𝑛 𝑥 − 𝑥0 𝑛 P0 𝑥 𝑑2 𝑦 𝑑𝑥2 +P1 𝑥 𝑑𝑦 𝑑𝑥 +P2 ( 𝑥)𝑦 = 0 where Po ( 𝑥) ≠ 0 𝑑2 𝑦 𝑑𝑥2 + P1 𝑥 𝑃0 𝑥 𝑑𝑦 𝑑𝑥 + 𝑃2 𝑥 𝑃0 𝑥 𝑦 = 0
- 3. Classification Of Singularity Analytic Function: A function 𝑓(𝑥) is said to be analytic at point 𝑥0 if 𝑓(𝑥) has Taylor Series Expansion about point 𝑥0 given by 𝑓 𝑥 = 𝑛=0 ∞ 𝑓 𝑛 𝑥0 𝑛! 𝑥 − 𝑥0 𝑛 exists and converges to 𝑓 𝑥 . If a function 𝑓(𝑥) is not analytic at point 𝑥0 , then it is called a Singular Point. Ordinary Point : A point 𝑥 = 𝑥0 is said to be an ordinary point of equation: 𝑑2 𝑦 𝑑𝑥2 + 𝑃 𝑥 𝑑𝑦 𝑑𝑥 + 𝑄 𝑥 𝑦 = 0 , if both P(𝑥) and Q(𝑥) are analytic at point 𝑥0.
- 4. Singular Point: A point 𝑥0 is said to be a singular point of equation: 𝑑2 𝑦 𝑑𝑥2 + 𝑃 𝑥 𝑑𝑦 𝑑𝑥 + 𝑄 𝑥 𝑦 = 0 , if both P(𝑥) and Q(𝑥) are analytic at point 𝑥0. A point 𝑥 is 𝑥0 that is not an ordinary point ,then it is called a Singular Point. SINGULAR POINTS CLASSIFICATION Singular points are classified as: 1. Regular Singular Point 2. Irregular Singular Point
- 5. 1.Regular Singular Point: A singular point 𝑥 = 𝑥0 is said to be regular singular point of equation : 𝑑2 𝑦 𝑑𝑥2 + 𝑃 𝑥 𝑑𝑦 𝑑𝑥 + 𝑄 𝑥 𝑦 = 0 , If both term 𝑥 − 𝑥0 𝑃(𝑥) and 𝑥 − 𝑥0 2 𝑄 𝑥 are analytic at point 𝑥0. 2.Irregular Singular Point: If 𝑥 − 𝑥0 𝑃(𝑥) and 𝑥 − 𝑥0 2 𝑄(𝑥) or both are not analytic, then it is called Irregular singular point.