Course teached as: B014739 - ANALISI NUMERICA 3-years First Cycle Degree (DM 270/04) in MECHANICAL ENGINEERING Curriculum SCIENTIFICO-MECCANICO
The Matlab environment and programming language. Direct methods for sparse linear systems. Iterative methods for nonlinear systems of equations. Newton-Cotes, composite and adaptive quadrature rules. Numerical methods for the Cauchy problem. Numerical methods for partial differential equations.
A. Quarteroni, R. Sacco, F. Saleri, Matematica numerica, Springer–Verlag.
J. Epperson, Introduzione all'analisi numerica,Teoria, metodi, algoritmi, Mc-Graw Hill.
Applying knowledge and understanding related to the choice and application of appropriate analytical and modelling methods, based on mathematical and numerical analysis, in order to better simulate the behavior of components and plants in order to predict and improve their performance.
Applying knowledge and understanding related to the appropriate interpretation of the results of experimental tests, verification calculations and complex theoretical simulation processes, through the use of the computer, applying the acquired experimental, modeling, mathematical and informatics bases.
Applying adequate knowledge and understanding to understand English texts.
In-depth knowledge and understanding of the theoretical-scientific aspects of mathematics and other basic sciences. To be able to use this knowledge to interpret and describe complex and/or interdisciplinary engineering problems.
Lectures and Matlab laboratory.
Type of Assessment
Oral exam on the numerical methods presented, their theoretical properties and implementation.
Matlab: environment and programming language. Direct factorization for sparse linear systems. Newton method and its variants, linesearch strategies. Newton-Cotes and composite quadrature rules.
One-step merical methods for the Cauchy problem: Runge-Kutta and Runge-Kutta-Fehlberg methods, some implicit schemes. Finite differences methods for partial differential equations. Method of lines for heat equation. Introduction to finite elements methods.