
Course unit
NUMERICAL ANALYSIS
SCP4063208, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/08 
Numerical Analysis 
7.0 
Course unit organization
Period 
Second 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 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
4 a.a 2018/2019 
01/10/2018 
28/02/2020 
REDIVO ZAGLIA
MICHELA
(Presidente)
MARTINEZ CALOMARDO
ANGELES
(Membro Effettivo)
CIPOLLA
STEFANO
(Supplente)
MARCUZZI
FABIO
(Supplente)
SOMMARIVA
ALVISE
(Supplente)

3 a.a. 2017/2018 
01/10/2016 
28/02/2019 
REDIVO ZAGLIA
MICHELA
(Presidente)
MARCUZZI
FABIO
(Membro Effettivo)
MARTINEZ CALOMARDO
ANGELES
(Membro Effettivo)
SOMMARIVA
ALVISE
(Membro Effettivo)

Prerequisites:

Basic knowledge of Mathematical analysis, Linear Algebra and Geometry (derivatives, vector spaces, vectors, matrices, operations, determinants, inverse matrix and particular matrices, scalar product, norms).
The courses on "Algebra and Discrete Matematics", "Mathematical Aanalysis" are formal prerequisites. 
Target skills and knowledge:

The student with this course
 will have the opportunity to acquire basic computer numerical skills;
 will be able to build the model and the numerical solution algorithm for simple mathematical problems;
 will be able to program with the language reference (Matlab) and also produce the results in graphic form;
 will acquire knowledge of some basic methods of Numerical Analysis in view of scientific and technological applications, with special attention to the concepts of error, discretization, data and functions approximation, convergence, stability, quadrature and ODE;
 will be able to apply the proposed methods on real life examples. 
Examination methods:

The exam is divided into two parts: written exam and laboratory test. There are five scheduled calls: summer session (two), autumn session (two) and winter recovery session (one).
 Written exam: During the written exam numerical analysis exercises are proposed to be carried out by hand, with the help of a nonprogrammable scientific calculator, keeping in mind the indications provided (use of exact arithmetic, use of approximate arithmetic, ...) and questions of understanding with a theoretical content. Each of the exercises and questions is assigned a score whose total will form the mark.
 Laboratory test: In each session, after the written exam, a test is carried out in the computer didactic laboratory, whose elaborations will be corrected and evaluated (insufficient, sufficient, good, excellent). The test is carried out in Matlab language and consists in the resolution of a simple numerical calculation problem with the development of script, function and possible production of graphs. The passing with sufficient, good or excellent evaluation of this test is a prerequisite for passing the exam.
 The oral exam is possible on request, but optional. 
Assessment criteria:

The evaluation criteria with which the knowledge and skills acquired will be verified are:
1  Knowledge of the various methods described both from the theoretical and algorithmic point of view.
2  Ability to apply the methods learned during the course to simple exercises of application.
3  Properties of the mathematical terminology used and correctness of exact resolution of the calculations.
4  Ability and familiarity in the use and writing of simple programs in the Matlab environment. 
Course unit contents:

 Computer Arithmetic
The numbers. Basis. FloatingPoint numbers and arithmetic. Errors in computation. Stability of algorithms. Condition number.
 Nonlinear Equations
Iterative methods. Convergent sequences. Existence and unicity theorems. Bisection algorithm. Fixed point iteration. Newton's methods. Methods for multiple roots. Stopping criteria.
 Numerical linear algebra
Linear systems; computational cost; errors and conditioning; estimate of the errors; preconditioning. Direct Methods for linear systems: Gauss and matrix factorizations. Cholesky method. Householder (hints). Matrix Inversion. Preconditioning. Iterative Methods for linear systems: Jacobi, GaussSeidel, SOR. Convergence theorems. Stopping criteria.
Eigenvalue and Eigenvectors (hints)
 Polynomial Approximation
Interpolation (Lagrange, Newton, Chebyshev). Convergence. Least squares approximation.
 Numerical Integration
Interpolatory formulae: Lagrange, NewtonCotes. Gauss (hints).
 Ordinary differential equations: Initial Value Problems. Implicit and Explicit one step methods (Taylor, Euler). 
Planned learning activities and teaching methods:

The course consists of lectures and exercises in the classroom (48 hours) and lessons in the computer lab (16 hours) with exercises on the computer in Matlab.
Many of the basic methods of numerical analysis presented during the lectures, will gradually be used in the laboratory in order to show their actual use and their potential.
Several laboratory exercises will be offered to students to integrate their learning at home.
Gradually the student will also become familiar with a programming environment for numerical problems and at the end of the course should be able to pass a test that is an integral part of the final exam.
During the course will be carried out activities of T4L (Teach for Learning) to improve learning and interaction teacher/student and student/student. 
Additional notes about suggested reading:

All the course's supplementary teaching material is available on the Moodle platform.
There are numerous online tutorials, manuals and online courses related to the Matlab programming environment.
On the teacher's website www.math.unipd.it/~michela
in the didactic section, it is possible to retrieve some links and information related to the free recovery of the Matlab software (the Patavian University has acquired a Campus License) 
Textbooks (and optional supplementary readings) 

Michela Redivo Zaglia, Calcolo Numerico: Metodi ed Algoritmi. Padova: Libreria Progetto, 2011. Quarta Edizione riveduta

Michela Redivo Zaglia, Calcolo Numerico: Esercizi. Padova: Libreria Progetto, 2015. Terza Edizione

Innovative teaching methods: Teaching and learning strategies
 Laboratory
 Interactive lecturing
 Working in group
 Peer feedback
 Loading of files and pages (web pages, Moodle, ...)
 Students peer review
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Matlab
Sustainable Development Goals (SDGs)

