SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS , Solution of equation , Fixed point iteration , Newton’s method , Gauss – Jacobi method , Solution of linear system by Gaussian elimination , Gauss – Jordon method , Gauss – Seidel method , Inverse of a matrix by Gauss Jordon method , Eigenvalue of a matrix by power method , Jacobi method for symmetric matrix , INTERPOLATION AND APPROXIMATION , Lagrangian Polynomials , Divided differences , Interpolating with a cubic spline , Newton’s forward difference formula , Newton’s backward difference formula , Differentiation using interpolation formulae , Numerical integration by trapezoidal rule , Simpson’s 1/3 and 3/8 rules Romberg’s method , Two and Three point Gaussian quadrature formulas , Double integrals using trapezoidal and simpsons’s rules , Taylor series method , Euler methods , Runge-Kutta method for solving first and second order equations , Milne’spredictor and corrector method , Adam’s predictor and corrector method , Finite difference solution of second order ordinary differential equation , Finite difference solution of one dimensional heat equation by explicit and implicit methods , One dimensional wave equation , Two dimensional Laplace equation , Poisson equation ,
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## UNIT I

## SOLUTION OF EQUATIONS AND

## EIGENVALUE PROBLEMS

## Solution of equation

## Fixed point iteration: x=g(x) method

## Newton’s method

## Solution of linear system by Gaussian elimination

## Gauss – Jordon method

## Gauss – Jacobi method

## Gauss – Seidel method

## Inverse of a matrix by Gauss Jordon method

## Eigenvalue of a matrix by power method

## Jacobi method for symmetric matrix.

##

## UNIT II

## INTERPOLATION AND APPROXIMATION

## Lagrangian Polynomials

## Divided differences

## Interpolating with a cubic spline

## Newton’s forward difference formula

## Newton’s backward difference formula

##

## UNIT III

## NUMERICAL DIFFERENTIATION AND

## INTEGRATION

## Differentiation using interpolation formulae

## Numerical integration by trapezoidal rule

## Simpson’s 1/3 and 3/8 rules

## Romberg’s method

## Two and Three point Gaussian quadrature formulas

## Double integrals using trapezoidal and simpsons’s rules.

## UNIT IV

INITIAL VALUE PROBLEMS FOR

ORDINARY DIFFERENTIAL EQUATIONS

Taylor series method

Euler methods

Runge-Kutta method for solving first and second order equations

Milne’spredictor and corrector method

Adam’s predictor and corrector method.

## UNIT V

BOUNDARY VALUE PROBLEMS IN

ORDINARY AND

PARTIALDIFFERENTIAL EQUATIONS

Finite difference solution of second order

ordinary differential equation

Finite difference solution of one dimensional

heat equation by explicit and implicit methods

One dimensional wave equation

Two dimensional Laplace equation

Poisson equation

INITIAL VALUE PROBLEMS FOR

ORDINARY DIFFERENTIAL EQUATIONS

Taylor series method

Euler methods

Runge-Kutta method for solving first and second order equations

Milne’spredictor and corrector method

Adam’s predictor and corrector method.

BOUNDARY VALUE PROBLEMS IN

ORDINARY AND

PARTIALDIFFERENTIAL EQUATIONS

Finite difference solution of second order

ordinary differential equation

Finite difference solution of one dimensional

heat equation by explicit and implicit methods

One dimensional wave equation

Two dimensional Laplace equation

Poisson equation

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