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
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
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.
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.
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