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# MA6459-NUMERICAL-METHODS-SYLLABUS-REGULATION-2013

MA6459                                NUMERICAL  METHODS                                        L T P C                                                                                                                                3 1 0 4

OBJECTIVES:

• 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

UNIT I             SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS          10+3

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                                     8+3

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                 9+3

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                                                                                                               9+3

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                                                                                     9+3

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.

TOTAL (L:45+T:15): 60 PERIODS

OUTCOMES:

• The students will have a clear perception of the power of numerical techniques, ideas and would be able to demonstrate the applications of these techniques to problems drawn from industry, management and other engineering fields.

TEXT BOOKS:

1. B.S.,   and   Grewal.   J.S.,”Numerical   methods   in   Engineering   and   Science”,           Khanna Publishers, 9th Edition, New Delhi, 2007.
2. C. F., and Wheatley. P. O., “Applied  Numerical  Analysis”, Pearson Education, Asia,

6th Edition, New Delhi, 2006.

REFERENCES:

1. S.C.,  and  Canale.R.P.,  “Numerical  Methods  for  Engineers,  Tata  McGraw  Hill, 5th Edition, New Delhi, 2007
2. Brian   “A  friendly  introduction  to  Numerical  analysis”,  Pearson  Education,  Asia,       New Delhi, 2007.
3. Sankara Rao. K., “Numerical methods  for Scientists  and  Engineers”, Prentice Hall of India Private, 3rd Edition, New Delhi, 2007.