First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
NUMERICAL ANALYSIS
SC06101050, 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
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2018/19
N0
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure http://matematica.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 ANGELES MARTINEZ CALOMARDO

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019
Show course schedule 2019/20 Reg.2008 course timetable

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)

Syllabus
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 ill-conditioning.

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, Gauss-Seidel 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. Cerca nel catalogo
  • Alfio Quarteroni, Fausto Saleri, Paola Gervasio., Calcolo scientifico: esercizi e problemi risolti con MATLAB e Octave. Milan [etc.]: Springer, 2017. Cerca nel catalogo
  • Rodriguez, Giuseppe, Algoritmi numerici. Bologna: Pitagora, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Laboratory

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Matlab