
Course unit
NUMERICAL ANALYSIS
SC06101050, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2017/18
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 
8 Calcolo Numerico  a.a. 2018/2019 (modif. 05/06/2019) 
01/10/2018 
30/09/2019 
SOMMARIVA
ALVISE
(Presidente)
MARCUZZI
FABIO
(Membro Effettivo)
DE MARCHI
STEFANO
(Supplente)
MARTINEZ CALOMARDO
ANGELES
(Supplente)
PUTTI
MARIO
(Supplente)

Prerequisites:

Calculus, Basic Linear Algebra. 
Target skills and knowledge:

In this course students learn the essential numerical techniques which are commonly used in scientific applications, when these have to face with mathematical problems that can not be solved analytically. Students are introduced to the basic computational concepts of stability, accuracy and efficiency.
It is also a goal of this course to introduce the students to the fundamental concepts of scientific programming using MATLAB. 
Examination methods:

Written exam and programming test. Oral exams could be possible in some cases. 
Assessment criteria:

The final grade will be based on the ability to clearly and correctly expose the theoretical contents explained in the course through a written exam.
Besides a practical programming test must be passed. The programming test is designed to assess the ability of the students of writing efficient implementations of the introduced numerical algorithms as well as using them to solve given problems.
Original solutions to the proposed exercises and programs providing any improvement to the implementations discussed during the course will be evaluated positively.
The final grade will be obtained by adding to the written test grade a maximum of two points proportionally to the final grade of the practical part. 
Course unit contents:

Fundamental principles of digital computing and the implications for algorithm accuracy and stability: Number representation. IEEE standard. Error propagation, cancellation, stability and illconditioning.
Introduction to computational complexity.
Several lectures are devoted to solving nonlinear equations: the bisection method, error estimation. The Newton method, global and local convergence, how to terminate Newton's iterations. Other linearization methods. Fixed point iterations. Stopping criteria for fixed point iterations.
The concept of interpolation and its role as foundation for numerical integration is introduced, emphasizing classical Lagrange polynomial interpolation. Error and convergence analysis. Piecewise polynomial interpolation: Spline. Least squares approximation.
Numerical differentiation and integration: Finite difference approximations to derivatives. Local error, error cancellation, and global error. Extrapolation. Trapezoidal rule, Simpson's rule. Error bounds.
The solution of systems of linear equations, (comprising 90% of numerical effort in science and engineering) is covered extensively, including direct (Gaussian elimination) and iterative techniques: vector and matrix norms, condition number of a system of linear equations, condition number of a matrix.
The LU factorization and it's use for solving systems of linear equations. Computing the factors by Gaussian elimination.
Stability. Pivoting. QR factorization and the accurate solution of overdetermined systems arising from least squares problems.
Classical iterative methods: Jacobi, GaussSeidel and Successive Overrelaxation.
An important component of the course is computational implementation of the studied numerical algorithms in order to observe first hand the issues of convergence, accuracy, computational work effort, and stability. Exercises will consist entirely in computational experiments in MATLAB. 
Planned learning activities and teaching methods:

Theoretical lectures.
Practical computer sessions.
Learning material will be donwloadable from the Moodle platform of the Department of Mathematics. 
Additional notes about suggested reading:

One of the suggested handbooks.
Online material can be obtained from:
www.math.unipd.it/~acalomar (alla voce Didattica)
and the Moodle platform of the Department of Mathematics, mainly regarding exercises and learning material for the computer sessions. 
Textbooks (and optional supplementary readings) 

Quarteroni, Alfio; Saleri, Fausto., Calcolo scientifico: esercizi e problemi risolti con MATLAB e Octave. Milano: Springer, 2012.

Alfio Quarteroni, Fausto Saleri, Paola Gervasio., Calcolo scientifico: esercizi e problemi risolti con MATLAB e Octave. Milan [etc.]: Springer, 2017.

Rodriguez, Giuseppe, Algoritmi numerici. Bologna: Pitagora, .

Innovative teaching methods: Teaching and learning strategies
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Matlab

