35433 - NUMERICAL METHODS

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

• 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