First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
NUMERICAL ANALYSIS
SC06101050, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2014/15

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2015/16
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/2015/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 MARCO VIANELLO MAT/08
Other lecturers ANGELES MARTINEZ CALOMARDO 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 01/10/2015
End of activities 28/01/2016

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)
6 Calcolo Numerico - 2016/2017 01/10/2016 30/09/2017 VIANELLO MARCO (Presidente)
MARTINEZ CALOMARDO ANGELES (Membro Effettivo)
DE MARCHI STEFANO (Supplente)
MARCUZZI FABIO (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
5 Calcolo Numerico - a.a. 2015/2016 01/10/2015 30/09/2016 VIANELLO MARCO (Presidente)
MARTINEZ CALOMARDO ANGELES (Membro Effettivo)
DE MARCHI STEFANO (Supplente)
MARCUZZI FABIO (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)

Syllabus
Prerequisites: Mathematical analysis 1, Geometry 1
Target skills and knowledge: Learning numerical computing fundamentals in view of scientific and technological applications, with special attention to the concepts of error, discretization, approximation, convergence, stability, computational cost
Examination methods: Written exam and possible oral exam
Assessment criteria: Oral exam with score range 18-23 in the written exam, or by student's choice with score > 23 in the written exam
Course unit contents: Floating-point sistem and error propagation

Computational complexity by examples

Numerical solution of nonlinear equations

Interpolation and approximation of functions and data

Numerical integration and differentiation

Elements of numerical linear algebra
Planned learning activities and teaching methods: Floating-point system and error propagation:
truncation and rounding error, floating-point representation of reals, machine precision, operations with approximate numbers, conditioning of functions, error propagation in iterative algorithms, the concept of stability

Computational complexity by examples:
Hoerner scheme for polynomials, fast power evaluation by binary coding of the exponent, computing the function exp, determinant by the gaussian elimination method

Numerical solution of nonlinear equations:
bisection method, error estimate by the weigthd residual; Newton method, global convergence, convergence rate, local convergence, error estimate, other linearization methods; fixed-point iterations

Interpolation abd approximation of functions and data:
polynomial interpolation, Lagrange interpolation, interpolation error, the convergence problem (Runge's counterexample), Chebyshev interpolation, stability of interpolation; piecewise polynomial interpolation, spline interpolation; least-squares polynomial approximation

Numerical integration and differentiation:
algebraic and composite formulas, convergence and stability, examples; instability of differentiation, computing derivatives by difference formulas; the concept of extrapolation

Elements of numerical linear algebra:
vector and matrix norms, conditioning of matrices and systems; direct methods: Gaussian elimination method and LU factorization, computing the inverse matrix, QR factorization, least-squares solution of overdetermined systems

Laboratory: implementation and application of numerical codes in Matlab
Additional notes about suggested reading: one of the suggested textbooks and online notes of the lecturer (www.math.unipd.it/~marcov/studenti.html)
Textbooks (and optional supplementary readings)
  • A. Quarteroni, F. Saleri, Introduzione al calcolo scientifico. --: Springer, --. Cerca nel catalogo
  • A. Quarteroni, F. Saleri, Scientific computing with Matlab and Octave. --: Springer, --. for Erasmus students Cerca nel catalogo
  • G. Rodriguez, Algoritmi numerici. --: Pitagora, --. Cerca nel catalogo