MA 6459 Numerical Methods Notes Pdf or M4 Maths Notes Anna University 4th Semester maths Notes are available here. All the five units subject of the lecture Notes is covered.

## Numerical Methods Notes pdf – Lecture Notes/Study Materials

Numerical Methods Lecture Notes are as per Anna University syllabus from regulation 2013 and having important two marks and sixteen marks Questions with Answers in separate units here.

## MA 6459 Numerical Methods Notes pdf – M4 Maths Notes

Numerical Methods Notes pdf for M4 4th Sem Notes. This course aims at providing the necessary basic concepts of a few numerical methods and give procedures for solving numerically different kinds of problems occurring in engineering and technology

## Numerical Methods Study Materials

Method of False position (Or) Regula-Falsi method (Or) Linear interpolation method

In bisection method the interval is always divided into half. If a function changes sign over an interval, the function value at the midpoint is evaluated. In bisection method the interval from a to b into equal intervals ,no account are taken of the magnitude of .An alternative method that exploits this graphical insights is to join by a straight line.

The intersection of this line with the X-axis represents an improved estimates of the root.The replacement of the curve by a straight line gives a “false position” of the root is the origin of the name ,method of false position ,or in Latin ,Regula false .It is also called the linear interpolation method.

UNIT- I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method- Solution of linear system of equations – Gauss elimination method – Pivoting – Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel – Matrix Inversion by Gauss Jordan method – Eigen values of a matrix by Power method

UNIT – II INTERPOLATION AND APPROXIMATION

Interpolation with unequal intervals – Lagrange’s interpolation – Newton‟s divided difference interpolation – Cubic Splines – Interpolation with equal intervals – Newton‟s forward and backward difference formulae.

UNIT – III NUMERICAL DIFFERENTIATION AND INTEGRATION

Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson‟s 1/3 rule – Romberg‟s method – Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson‟s 1/3 rules.

UNIT- IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Single Step methods – Taylor‟s series method – Euler‟s method – Modified Euler‟s method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods – Milne‟s and Adams-Bash forth predictor corrector methods for solving first order equations.

UNIT- V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

Finite difference methods for solving two-point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace‟s and Poisson‟s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.

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