73513 - NUMERICAL METHODS M

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.

Contenuti

• Key idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.

• Solution to nonlinear equations.

• Numerical Linear Algebra: direct methods for linear systems.

• Linear least squares.

• Polynomial interpolation.

• Numerical differentiation.

• Classification of PDEs: elliptic, parabolic and hyperbolic equations.

• Finite difference methods. Stability, consistency, and convergence theory.

Testi/Bibliografia

• U. Ascher, C. Greif, A first course in Numerical Methods, SIAM, 2011.

• A. Quarteroni, R. Sacco and F. Saleri, "Numerical Mathematics, Second Ed.", Springer, 2007.

• M.T. Heath, "Scientific Computing. An introductory survey", McGraw-Hill, 1997.

Metodi didattici

The course involves theoretical lectures and practical work based on computational tools such as Matlab.

Modalità di verifica e valutazione dell'apprendimento

Assessment is based on a written exam including exercises with Matlab and written questions.

Strumenti a supporto della didattica

Lectures, lecture slides, exercises, laboratory activities with Matlab and possibly other softwares.

Orario di ricevimento

Consulta il sito web di Carolina Vittoria Beccari