Lecturer: Tullio Facchinetti   Luisa Donatella Marini  

Course name: Calcolo numerico e programmazione
Course code: 502525
Degree course: Ingegneria Civile e Ambientale
Disciplinary field of science: ING-INF/05
L'insegnamento costituisce attività di base per: Ingegneria Civile e Ambientale
University credits: CFU 12
Course website: n.d.

Specific course objectives

The course is meant to make the students aquainted with the basic tools of Numerical Analysis and Programming. In particular, the most commonly used numerical algorithms to deal with practical problems will be illustrated, together with their practical implementation.

Course programme

The course is made of two modules: NUMERICAL ANALISIS and PROGRAMMING. These two modules complement each other. Classes and practical programming sessions are intended to develop from theory to practice all the subjects presented.

NUMERICAL ANALYSIS Module
The following is a list of the subjects which will be developed:

• Nonlinear equations: bisection and Newton's methods. Convergence and order of convergence. Stopping criteria.
• Functions and data approximation: Least square method for data fitting: linear regression and other examples.
• Numerical derivation and integration: Approximation of derivatives. Quadrature formulae: mid-point, trapezoidal, and Simpson rules, simple and composite. Hints on gaussian formulas.
• Direct methods for solving linear systems: Conditioning problem; eigenvalues problems. Gaussian elimination and LU factorization; Implementational aspects of LU factorization and costs; Simmetric and positive definite matrices: Cholesky factorization.
• Iterative methods for solving linear systems: Jacobi, Gauss-Seidel, and relaxation methods; Convergence results and implementational aspects; Stopping criteria.
• Numerical solution of ordinary differential equations: One-step methods: explicit and implicit Euler, Crank-Nicolson, Heun;Stability and A-stability, consistence, convergence and orders of convergence; Computational aspects.

COMPUTER PROGRAMMING Module

• Representation of information: binary and hexadecimal notation.
• Data types: integer and real number, string, array, matrix, file.
• Algorithms: fundamental, programming and debugging.
• Structured programminigFundamental control structures: loops and branches; procedures and functions.
• MatLab programming language: development kit, types of data, control structures, toolbox, file system, scientific visualization.

Course entry requirements

Integral and differential calculus for real functions; complex numbers; vectors and matrices. Basic computer usage skills.

Course structure and teaching

Lectures (hours/year in lecture theatre): 70
Practical class (hours/year in lecture theatre): 34
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

A. Quarteroni, F. Saleri. Introduzione al Calcolo Scientifico - II Edizione. Springer-Verlag Italia..

Adrian Biran, Moshe Breiner. MATLAB for engineers . Addison-Wesley.

Testing and exams

Two written intermediate exams, one at the end of the first semester on the first part of the course, and a second one at the end of the second semester on the second part of the course. Additional written exams on the whole program. Oral exam (not compulsory) after a sufficient grade in the written part. For details on both written and oral part see http://www.imati.cnr.it/marini

Examination to check the knowledge of the MatLab environment and programming language, as well as to check the knowledge of structured programming.