
Course unit
NUMERICAL ANALYSIS
SC06101050, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/08 
Numerical Analysis 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Laboratory 
1.0 
16 
9.0 
No turn 
Lecture 
5.0 
40 
85.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
9 Calcolo Numerico  a.a. 2019/2020 
01/10/2019 
30/09/2020 
VIANELLO
MARCO
(Presidente)
PIAZZON
FEDERICO
(Membro Effettivo)
DE MARCHI
STEFANO
(Supplente)
MARCUZZI
FABIO
(Supplente)
SOMMARIVA
ALVISE
(Supplente)

Prerequisites:

Basic knowledge of mathematical analysis and linear algebra. 
Target skills and knowledge:

Learning the base of numerical computing in view of scientific and technological applications, with special attention to the concepts of error, discretization, approximation, convergence, stability, computational cost. 
Examination methods:

Written exam and laboratory exam. 
Assessment criteria:

The written exam aims at verifying the comprehension of the theoretical foundations of numerical methods.
The laboratory exam aims at verifying the implementation and application capabilities of numerical algorithms. 
Course unit contents:

Floatingpoint system and error propagation:
truncation and rounding error, floatingpoint representation of real numbers, machine precision, arithmetical operations with approximate numbers, conditioning of functions, error propagation within iterative algorithms by examples, the concept of stability.
Numerical solution of nonlinear equations:
bisection method, error estimate by weighted residuals; Newton method, global convergence, order of convergence, local convergence, error estimate, other linearization methods; fixedpoint iterations.
Interpolation and approximation of functions and data:
polynomial interpolation, Lagrange interpolation, interpolation error, the convergence problem (Runge's counterexample), Chebyshev interpolation, stability of interpolation; piecewise polynomial interpolation, spline interpolation; leastsquares polynomial approximation.
Numerical integration and differentiation:
algebraic and composite quadrature formulas, convergence and stability, examples; instability of differentiation, derivatives computation by difference formulas; the concept of extrapolation.
Elements of numerical linear algebra:
vector and matrix norms, matrix and system conditioning; direct methods: Gaussian elimination and LU factorization, computation of inverse matrices, QR factorization, leastsquares solution of overdetermined systems; introduction to iterative methods.
Laboratory: implementation and application of numerical codes in Matlab. 
Planned learning activities and teaching methods:

Classroom lessons and laboratory exercises. 
Additional notes about suggested reading:

Suggested textbook and online teacher notes
(www.math.unipd.it/~marcov/studenti.html). 
Textbooks (and optional supplementary readings) 

A. Quarteroni et al., Introduzione al Calcolo Scientifico. : Springer (una delle edizioni recenti), .

G. Rodriguez, Algoritmi Numerici. : Pitagora, .

A. Quarteroni et al., Scientific computing with Matlab and Octave. : Springer, . for foreign students

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Laboratory
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used

