# MA1251 – NUMERICAL METHODS

MA1251  –  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
TEXT BOOKS
1.         Veerarjan,  T  and  Ramachandran,  T.,  “Numerical  Methods  with  Programming
in C”, 2nd Editiion, Tata McGraw-Hill Publishing Co.Ltd, 2007.
2.         Sankara Rao, K, “Numerical Methods for Scientisits and Engineers”, 3rd Edition,
Printice Hall of India, 2007.

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