Numerical Analysis

Course Code: MAT 323

Credit Hour: 3

Course Group: Mathematics

Polynomials: Numerical solution of polynomials. Computational methods for solving problems in linear algebra, linear programming, nonlinear equations,

Solution of Algebraic and Transcendental Equation: Solution of Algebraic and Transcendental Equation using Graphical method, Analytical method, Regular falsi method, Iteration  &  Newton’s Raphson method. Simultaneous Linear Algebraic Equation: Solution of simultaneous linear algebraic equation using Matrix inverse method, Cramer’s method, Gauss elimination method, Crouts method, Factorization method and Gauss Seidel iterative method. Interpolation with Equal Interval: Different interpolation method, Graphical method, Method of curve fitting method. Interpolation with Unequal Interval: Divided difference method, Newton’s formulae for unequal interval, Relation between divided difference and ordinary difference, Lagrange’s interpolation formula unequal interval & Hermite’s interpolation formula. Errors:  Errors and their analysis; absolute, relative and percentage errors; remainder terms of various interpolation formulae. Numerical Integration: General quadrature formula, Trapezoidal rule, Simpson’s one third-three-eight rule, Weddle’s rule, Cote’s method, Numerical double and Gaussian Integration. Numerical Solution of Ordinary Diff. Equation: Pichards method, Euler method, Taylor’s method, Rungs method, Rungs-Kutta method. Curve Fitting and Principle of least-squares.  Scatter diagram, Methods of curve fitting- Grapgic method, Method of Least Square, Change of origin and scales,  Most plausible solution og a system of linear equations, Fitting  of the curve of type y = ab^x, y = ax^b, pv^r = k. Eigen Value and Eigen Vectors: Iterative method for dominant latent root, Evaluation of all the eigen values, the eigen values of real symmetric  matrix, Given’s method.

Reference Books:

1. S. Balachandra Rao and C.K. Shantha :  Numerical Methods
2. Ferziger and J.H :  Numerical Methods for Engineering Application.
3. Gerald and C.F.:  Applied Numerical Analysis.