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

MA6459 Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â NUMERICALÂ  METHODSÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  L T P C Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â 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 IÂ Â Â Â Â Â Â Â Â Â Â Â  SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS Â  Â  Â  Â  Â 10+3

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

UNIT IIÂ Â Â Â Â Â Â Â Â Â Â  INTERPOLATIONÂ  ANDÂ  APPROXIMATION Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  8+3

Interpolation with unequal intervals – Lagrange’s interpolation â Newtonâs divided difference interpolation â Cubic Splines – Interpolation with equal intervals – Newtonâs forward and backward difference formulae.

UNIT IIIÂ Â Â Â Â Â Â Â Â Â  NUMERICALÂ  DIFFERENTIATIONÂ  ANDÂ  INTEGRATION Â  Â  Â  Â  Â  Â  Â  Â  9+3

ApproximationÂ Â  ofÂ Â  derivativesÂ Â  usingÂ Â  interpolationÂ Â  polynomialsÂ Â  –Â Â  NumericalÂ Â  integrationÂ Â  using Trapezoidal,Â  SimpsonâsÂ  1/3Â  ruleÂ  âÂ  RombergâsÂ  methodÂ  –Â  TwoÂ  pointÂ  andÂ  threeÂ  pointÂ  Gaussian quadrature formulae â Evaluation of double integrals by Trapezoidal and Simpsonâs 1/3 rules.

UNIT IVÂ Â Â  Â INITIALÂ  VALUEÂ  PROBLEMSÂ  FOR ORDINARYÂ  DIFFERENTIAL EQUATIONS Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

Single Step methods – Taylorâs series method – Eulerâs method – Modified Eulerâs method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods – Milneâs and Adams- Bash forth predictor corrector methods for solving first order equations.

UNIT VÂ Â Â Â Â Â Â Â Â Â  BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

Finite difference methods for solving two-point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplaceâs and Poissonâs equations on rectangular domain â One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods â 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.,Â Â  andÂ Â  Grewal.Â Â  J.S.,”NumericalÂ Â  methodsÂ Â  inÂ Â  EngineeringÂ Â  andÂ Â  Science”, Â  Â  Â  Â  Â  Khanna Publishers, 9th Edition, New Delhi, 2007.
2. C. F., and Wheatley. P. O., “AppliedÂ  NumericalÂ  Analysis”, Pearson Education, Asia,

6th Edition, New Delhi, 2006.

REFERENCES:

1. S.C.,Â  andÂ  Canale.R.P.,Â  “NumericalÂ  MethodsÂ  forÂ  Engineers,Â  TataÂ  McGrawÂ  Hill, 5th Edition, New Delhi, 2007
2. Brian Â  “AÂ  friendlyÂ  introductionÂ  toÂ  NumericalÂ  analysis”,Â  PearsonÂ  Education,Â  Asia, Â  Â  Â  New Delhi, 2007.
3. Sankara Rao. K., “Numerical methodsÂ  for ScientistsÂ  andÂ  Engineers”, Prentice Hall of India Private, 3rd Edition, New Delhi, 2007.

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MA6459 NUMERICAL METHODS SYLLABUS REGULATION 2017