First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
COMPUTER SCIENCE
Course unit
NUMERICAL ANALYSIS
SCP4063208, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
COMPUTER SCIENCE
SC1167, Degree course structure A.Y. 2011/12, A.Y. 2018/19
N0
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure http://informatica.scienze.unipd.it/2018/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MICHELA REDIVO ZAGLIA MAT/08
Other lecturers ANGELES MARTINEZ CALOMARDO MAT/08

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019

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)

Syllabus
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 non-programmable 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. Floating-Point 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, Gauss-Seidel, SOR. Convergence theorems. Stopping criteria.
Eigenvalue and Eigenvectors (hints)
- Polynomial Approximation
Interpolation (Lagrange, Newton, Chebyshev). Convergence. Least squares approximation.
- Numerical Integration
Interpolatory formulae: Lagrange, Newton-Cotes. 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 Cerca nel catalogo
  • Michela Redivo Zaglia, Calcolo Numerico: Esercizi. Padova: Libreria Progetto, 2015. Terza Edizione Cerca nel catalogo

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)
Quality Education Gender Equality