- Docente: Fiorella Sgallari
- Crediti formativi: 6
- SSD: MAT/08
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
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Corso:
Laurea Magistrale in
Ingegneria per l'ambiente e il territorio (cod. 8894)
Valido anche per Laurea Magistrale in Ingegneria chimica e di processo (cod. 8896)
Conoscenze e abilità da conseguire
A successful learner from this course will be able to: a) deal with numerical analysis topics such as: accuracy, truncation and round-off errors, condition numbers, convergence, stability, curve-fitting, interpolation, numerical differentiation and integration, numerical linear algebra; b) deal with numerical methods for solving ordinary and partial differential equations, with finite difference and finite element methods for parabolic and elliptic partial differential equations, applications of computer programs to case studies derived from civil engineering practice.
Contenuti
Requirements/Prior knowledge
A prior knowledge and understanding of Linear Algebra, Calculus and some experience in programming are required to attend with profit this course.
Course Contents
· Key idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
· Numerical Linear Algebra: direct methods for linear systems.
· Solution to single equations and multiple non-linear equations.
· Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.
· Numerical differentiation.
· Classification of PDEs: elliptic, parabolic and hyperbolic equations.
· Finite difference methods. Stability, consistency, and convergence theory.
Testi/Bibliografia
Some useful course materials for this course can be found at the web page http://www.dm.unibo.it/~sgallari at the link Teaching.
You can find the material for this course in many books on Numerical Analysis such as
- Uri Ascher and Chen Greif , A First Course in Numerical Methods , SIAM, 2011.
- A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics Second Ed.,,Springer, 2007.
Metodi didattici
The course involves practical work based on computational tools such as Matlab.
Modalità di verifica e valutazione dell'apprendimento
Assessment is based on assignments of project works and oral exams.
Strumenti a supporto della didattica
Lectures, exercises, laboratory activities in Matlab and other softwares.
Link ad altre eventuali informazioni
http://www.dm.unibo.it/~sgallari/
Orario di ricevimento
Consulta il sito web di Fiorella Sgallari