


Politecnico di Torino  
Academic Year 2007/08  
02GQRBP Numerical methods for differential problems 

Master of sciencelevel of the Bologna process in Telecommunication Engineering  Torino 





Objectives of the course
The aim of the course is to provide the basic knowledge for the numerical treatment of the following problems:
 solution of linear systems;  computation of eigenvalues and eigenvectors;  solution of boundary value problems for ordinary differential equations;  solution of boundary and initial value problems for partial differential equations. Some numerical methods will be applied to particular problems by using MATLAB, so that the students may understand their purpose and limitations. 
Expected skills
Knowledge of the basic concepts and characteristics of the illustrated methods.
Ability of applying the theoretical knowledge for solving real problems by means the MATLAB software. 
Prerequisites
Mathematical analysis, geometry, a basic course of numerical analysis.

Syllabus
Syllabus
Matrix decompositions and their applications. Numerical solution of symmetric and positive definite systems and Toeplitz systems. Finite difference methods, collocation and Galerkin methods for ordinary and partial differential equations. Syllabus: more informations Gauss, Choleski, QR, SVD decompositions and their applications in solving linear systems, in the computation of the determinant, of the rank and of the inverse of a matrix, in the least square solution of linear systems, in the computation of eigenvalues. The conjugate gradient method and the Levinson and Durbin methods. Finite difference methods, collocation and Galerkin method for boundary value problems of ordinary differential equations. Finite difference methods for boundary and initial value problems of partial differential equations. 
Laboratories and/or exercises
Classroom: exercises aimed at a deeper understanding of the topics.
Laboratory: in some practical sessions the students will apply (using MATLAB) the methods introduced during the lectures. 
Bibliography
Bibliography
D. Bini, M. Capovani, O. Menchi, Metodi numerici per l'algebra lineare, Zanichelli, Bologna, 1988. G. H. Golub, C. F. Van Loan, Matrix computations, Hohn Hopkins University Press, Baltimore, 1983. G. Monegato, Fondamenti di calcolo numerico, CLUT Editrice, Torino, 1998. 
Revisions / Exam
Written examination with both practical exercises and theoretical questions concerning all the topics of the program of the course. 
