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NUMERICAL CALCULUS AND PROGRAMMING

Degree course Electronic Engineering
Curriculum Curriculum unico
Learnings Orientamento unico
Academic Year 2018/2019
ECTS 6
Scientific Disciplinary Sector MAT/08
Year First year
Time unit Second semester
Class hours 48
Educational activity Related and integrative training activities

Single group

Supplying course 50M006 CALCOLO NUMERICO E PROGRAMMAZIONE in Ingegneria Informatica e dei sistemi per le Telecomunicazioni LM-27 COTRONEI MARIANTONIA
Professor Mariantonia COTRONEI
Objectives Aim of the course is to provide the basic knowledge of the main methods in Numerical Calculus and to introduce Matlab and Octave as environments for scientific computing. The educational objectives include the acquisition of: ability to construct numerical models and to design algorithms for their solution; awareness of the problems connected to the use of a computer for solving mathematical problems; ability towards computer implementation of numerical algorithms on the computer, to realize numerical tests and to critically analyse the results.
Programme FLOATING-POINT ARITHMETIC AND ERROR ANALYSIS
Computer representation of real numbers. Numerical accuracy. Floating-point arithmetic. Errors and error propagation. Conditioning of a mathematical problem. Algorithmic stability.

SOLUTION OF NON-LINEAR EQUATIONS
Iterative methods: convergence and convergence order. The bisection method. Newton-Raphson method: error analysis and error estimation. Secant method. Fixed point iteration. Stopping criteria.

SOLUTION OF SYSTEMS OF LINEAR EQUATIONS
Matrix arithmetic. Special matrices and their properties. Vector and matrix norms. Stability in solving linear systems. Condition number of a matrix.
Direct methods. Solution of triangular systems. Gauss elimination. Pivoting. LU factorization. Cholesky factorization. Iterative methods. Iteration matrix. Convergence. Stopping criteria. Jacobi and Gauss-Seidel methods. Richardson methods. Gradient and preconditioned gradient methods.

FUNCTION AND DATA APPROXIMATION
Polynomial interpolation. Lagrange polynomial. Interpolation error. Runge phenomenon. Spline interpolation. Linear and cubic splines.
Least square approximation.

NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives. Finite differences.
Interpolatory quadrature formulas. Order of exactness. Newton-Cotes and composite Newton-Cotes rules. Error formulas. Gauss-Legendre quadrature. Richardson extrapolation.

SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Cauchy problem. One-step methods. Local and global errors. Consistency and convergence. Euler and Crank-Nicolson methods. Runge-Kutta methods.
Multistep methods. AdamsBashforth and AdamsMoulton methods. Predictor-corrector schemes.

NUMERICAL METHODS FOR BOUNDARY VALUE PROBLEMS
Finite difference approximation of the Poisson problem in one and two dimensions. Finite element method. Finite element approximation of the Poisson problem in one dimension.

AN INTRODUCTION TO MATLAB
Main commands, arrays, built-in functions. Graphics. Design and development of programs.
Implementation of numerical methods and analysis/validation of the results on test problems.
Books A. Quarteroni, F. Saleri, P. Gervasio. Calcolo Scientifico. Esercizi e problemi risolti con MATLAB e Octave, Springer, 2012.
M.L. Lo Cascio, Fondamenti di Analisi Numerica, McGraw Hill, 2007.
G. Naldi, L. Pareschi, Matlab: Concetti e Progetti, Apogeo, 2013.
Quarteroni, R. Sacco, F. Saleri. Matematica Numerica, Springer, 2008
A. Quarteroni, F. Saleri, P. Gervasio. Scientific Computing with MATLAB and Octave, Springer
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation No
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation No
Internship evaluation No
Evaluation in itinere No
Practice Test Yes

Further information

No document in this course

Office hours list:

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Office hours by: Mariantonia Cotronei
Martedi' 10-12
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