MA2264 NUMERICAL METHODS Syllabus

MA2264                                  NUMERICAL METHODS                                     L T P C
                                                                                                                                 3 1 0 4

UNIT I   SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS           9
Solution of equation –Fixed point iteration: x=g(x) method - Newton’s method –  Solution
of linear system by Gaussian elimination and Gauss-Jordon method–   Iterative method -
Gauss-Seidel method - Inverse of a matrix by  Gauss Jordon method – Eigen value of a
matrix by power method and by Jacobi method for symmetric matrix.



UNIT II   INTERPOLATION AND APPROXIMATION                           9
Lagrangian  Polynomials  –  Divided  differences  –  Interpolating  with  a  cubic  spline  –
Newton’s forward and backward difference formulas.

UNIT III   NUMERICAL DIFFERENTIATION AND INTEGRATION                     9
Differentiation  using  interpolation  formulae  –Numerical  integration  by  trapezoidal  and
Simpson’s  1/3  and  3/8  rules  –  Romberg’s method  –  Two  and  Three  point Gaussian
quadrature formulae – Double integrals using trapezoidal and Simpsons’s rules.  

UNIT IV   INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL  
                        EQUATIONS                                                                                              9          
Single step methods: Taylor series method – Euler   method  for  first order equation   –
Fourth  order  Runge  –  Kutta  method  for  solving  first  and  second  order  equations  –
Multistep methods: Milne’s and Adam’s predictor and corrector methods.

UNIT V   BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL          
                       DIFFERENTIAL EQUATIONS                                       9
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 and two dimensional Laplace and Poisson equations.

L : 45 , T : 15 ,TOTAL = 60 PERIODS
TEXT BOOKS:

1.   Veerarajan, T and Ramachandran, T.  ‘Numerical methods with programming  in  ‘C’
Second Editiion, Tata McGraw-Hill Publishing.Co.Ltd. (2007).
2.    Sankara  Rao  K,  ‘Numerical  Methods  for  Scientisits  and  Engineers’  –  3rd
  editiion
Printice Hall of India Private Ltd, New Delhi, (2007).

REFERENCES:

1.  Chapra, S. C and Canale, R. P. “Numerical Methods for Engineers”, 5th
 Edition,  
      Tata McGraw-Hill, New Delhi, 2007.
2.  Gerald, C. F. and Wheatley, P.O., “Applied Numerical Analysis”, 6th
 Edition,  
      Pearson Education Asia, New Delhi, 2006.
3.  Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”,  
      6th
 Edition, Khanna Publishers, New Delhi, 2004