NUMERICAL METHODS AND COMPUTATION Syllabus

1.    Approximation in numerical computation: Truncation and rounding errors, fixed and floating point arithmetic, Propagation of errors.

2.    Interpolation: Newton forward/backward interpolation, Lagrange’s and Newton’s divided difference Interpolation

3.    Numerical Integration: Trapizoidal rule, Simpson’s 1/3 rule, Expression for corresponding error terms.

4.    Numerical solution of a system of linear equations: Gauss elimination method, matrix inversion, LU factorization method, Gauss-Seidel iterative method.

5.    Numerical solution of Algebraic equation: Bisection method, Regula-Falsi method, Newton-Raphson method. Numerical solution of Ordinary differential equation: Euler’s method, Runge-Kutta methods, Predictor-Corrector methods and Finite Difference method, Finite Volume method.