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.
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.
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.
