## Numerical Analysis I and Laboratory

Code no:

**9.2.08.4.1.9****, (9041)**Semester:**3th**, Teaching hours: 5## Core syllabus

Computer arithmetic, approximation and errors, floating point arithmetic, order of approximation and convergence, propagation of the errors difference operators.

Workshop exercises and programming in the PC-Lab using Matlab and Mathematica.

*Linear systems:*Gauss elimination method and factorization type methods. Computation of the inverse and determinant of a matrix. Iterative methods, fixed point method, Jacobi, Gauss-Seidel and Relaxation methods. Computation of eigenvalues and eigenvectors, power method.*Non linear equations and systems:*Bisection method, General iterative method, Newton-Raphson and Quasi-Newton methods, Secant and Regula-Falsi methods, Newton-Raphson and Quasi-Newton methods for non linear systems.*Interpolation and Approximation:*The problem of interpolation, Lagrange interpolation, Newton interpolation, Hermite interpolation, Piecewise interpolation and Spline interpolation. Least Squares approximation, discrete Least Squares approximation, continuous Least Squares approximation.*Numerical Differentiation and Integration:*Approximation of derivatives, Approximation of finite integral, basic rules for numerical integration, Composite Trapezoidal and Simpson integration formulas, Hermite and Gauss integration.Workshop exercises and programming in the PC-Lab using Matlab and Mathematica.