Course teached as: B026255 - METODI NUMERICI PER L'INGEGNERIA Second Cycle Degree in ENVIRONMENTAL ENGINEERING (POSTGRADUATE)
Teaching Language
Italian
Course Content
Finite precision computation.
Numerical methods for nonlinear equations.
Numerical solution of linear systems.
Data and function approximation.
Numerical integration. Numerical methods for initial value problems for ordinary differential equations. Finite difference methods for boundary value problems. Matlab programming language (only for Analisi Numerica e Programmazione (CIVILE) e Metodi numerici per l'ingegneria (AMBIENTE)).
M.G. Gasparo, R. Morandi, Elementi di Calcolo Numerico, McGraw Hill, 2008.
A.Quarteroni, R. Sacco, F. Saleri : Matematica Numerica. Springer-Verlag Italia,1998
W. Palm III : Matlab7 per l'Ingegneria e le scienze. Mc-Graw Hill, 2005.
C.F. Van Loan Introduction to Scientific Computing, Prentice Hall
Learning Objectives
Knowledge of the most used numerical methods for mathematical problems arising in the applications. Ability to develop an algorithm for the methods studied.
Prerequisites
Basic linear algebra tools: vectors, matrices, linear systems. Fundamental of Mathematical Analysis.
Teaching Methods
Lectures and Matlab laboratory (only for Analisi Numerica e Programmazione (CIVILE) e Metodi numerici per l'ingegneria (AMBIENTE)).
Type of Assessment
Written exam, the cut score for passing is 18/30.
After passing the written exams, the oral exam can be requested by the student.
Course program
Algorithms. Floating point arithmetics. Finite precision.
Conditioning of a problem.
Stability of an algorithm. Direct methods for linear systems: Gauss method and pivoting strategies,
Cholesky method. Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; corresponding algorithms.
Polinomial interpolation, spline interpolation.
Quadrature rules; composite Trapeziodal and Simpson rule; Rihardson extrapolation.
Numerical methods for initial value problems for differential equations: explicit one step methods (Euler and Runge-Kutta).
Finite difference methods for boundary value problems: central differences method and upwind method.