# MA8491 Syllabus Numerical Methods

## UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS MA8491 Syllabus Numerical Methods

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 – Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.

### UNIT II INTERPOLATION AND APPROXIMATION MA8491 Syllabus Numerical Methods

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

### UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION MA8491 Syllabus Numerical Methods

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 MA8491 Numerical Methods Syllabus

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 PARTIALDIFFERENTIAL EQUATIONS MA8491 Syllabus Numerical Methods

Finite difference methods for solving second order 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.

 Subject name NUMERICAL METHODS Short Name m4 Semester 4 Subject Code MA8491 Regulation 2017 regulation