First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
NUMERICAL ANALYSIS
SC06101050, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
N0
bring this page
with you
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/2017/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 MAT/08
Other lecturers MARCO VIANELLO MAT/08

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/08 Numerical Analysis 6.0

Mode of delivery (when and how)
Period First semester
Year 2nd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
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 02/10/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
7 Calcolo Numerico - 2017/2018 01/10/2017 30/09/2018 MARTINEZ CALOMARDO ANGELES (Presidente)
VIANELLO MARCO (Membro Effettivo)
DE MARCHI STEFANO (Supplente)
MARCUZZI FABIO (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (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: Oral exam due for students with overall grade after the written and lab tests in the range 18/30-23/30.
Course unit contents: Number representation and arithmetic operations on digital computing. Error propagation in arithmetic operations

Introduction to computational complexity

Numerical solution of nonlinear equations

Interpolation and data fitting

Numerical derivation and integration

Numerical linear algebra
Planned learning activities and teaching methods: 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 numerical analysis is computational implementation of algorithms which are developed in the course 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.
Additional notes about suggested reading: One of the suggested textbooks and online material provided by the instructors.
Useful links:
www.math.unipd.it/~acalomar (alla voce Didattica)
www.math.unipd.it/~marcov/studenti.html)
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
  • Quarteroni, Alfio; Saleri, Fausto, Scientific computing with MATLAB and OctaveAlfio Quarteroni, Fausto Saleri, Paola Gervasio. Berlin: Springer, 2014. For erasmus students. Cerca nel catalogo
  • Rodriguez, Giuseppe, Algoritmi numerici. Bologna: Pitagora, --. Cerca nel catalogo