italian version

Aims :

To provide the student with a good understanding of some basic numerical methods for solving mathematical problems that arise in computational science, engineering and mathematics so that he /she is able to choose appropriate techniques for solving problems and to interpret the results.

Topics :

1) Iterative Methods for the search of the roots of non linear equations. Algebraic equations. Sturm sequences, Bairstow scheme. Systems of non linear equations.
2) Direct and iterative schemes for the solution of systems of linear equations.
3) Polynomial interpolation (Lagrange, Newton, Chebyshev). Spline interpolation. Mean square polynomial approximation.
4) Numerical integration: Côtes integration formulae (simple and composite). Romberg Integration method. Gauss integration formulae .
5) Difference equations. Cauchy problems. Implicit and explicit Euler scheme, Crank-Nicolson. Runge-Kutta. Linear multistep methods. Convergence and stability .
6) Difference methods for PDE: Vibration Equation, Heat Equation, PoissonEquation.

To achieve the objectives, the student will be required to use MATLAB to implement numerical techniques and to study their properties.

Textbooks :

A.M. PERDON, Analisi Numerica, Pitagora Editrice, Bologna 2005
Lecture notes, exercises and information concerning the course can be found on the web site http://www.diiga.univpm.it/perdon.html.

Exam :

The final exam consists of a written test and an oral test.

Tutorial Session :

Monday and Wednesday from 14:30 to 16.30.