First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MECHANICAL ENGINEERING
Course unit
NUMERICAL ANALYSIS (Numerosita' canale 3)
IN18101050, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
MECHANICAL ENGINEERING
IN0506, Degree course structure A.Y. 2011/12, A.Y. 2018/19
N3cn3
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Degree course track Common track
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure http://im.dii.unipd.it/ingegneria-meccanica/
Department of reference Department of Industrial Engineering
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 ALVISE SOMMARIVA MAT/08
Other lecturers DAVIDE POGGIALI

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
IN18101050 NUMERICAL ANALYSIS (Canale A) ALVISE SOMMARIVA IN0515

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/08 Numerical Analysis 9.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
23 A.A. 2018/19 canale 2 01/10/2018 30/11/2019 DE MARCHI STEFANO (Presidente)
CAMPI CRISTINA (Membro Effettivo)
BERGAMASCHI LUCA (Supplente)
MARTINEZ CALOMARDO ANGELES (Supplente)
PUTTI MARIO (Supplente)
SOMMARIVA ALVISE (Supplente)
VIANELLO MARCO (Supplente)
22 A.A. 2017/18 01/10/2017 30/11/2018 DE MARCHI STEFANO (Presidente)
BERGAMASCHI LUCA (Supplente)
MARTINEZ CALOMARDO ANGELES (Supplente)
21 A.A. 2017/18 01/10/2017 30/11/2018 JANNA CARLO (Presidente)
MAZZIA ANNAMARIA (Membro Effettivo)
FERRONATO MASSIMILIANO (Supplente)

Syllabus
Prerequisites: Basic knowledge of mathematical analysis.
Target skills and knowledge: Learning the base of numerical computing 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 Matlab laboratory exam.
Assessment criteria: The mark is the weighted average of the written and laboratory test.
Course unit contents: Floating-point system and error propagation:
truncation and rounding error, floating-point representation of real numbers, machine precision, arithmetical operations with approximate numbers, conditioning of functions, error propagation within iterative algorithms by examples, the concept of stability

Numerical solution of nonlinear equations:
bisection method, error estimate by weighted residuals; Newton method, global convergence, order of convergence, local convergence, error estimate, other linearization methods; fixed-point iterations

Interpolation and 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 quadrature formulas, convergence and stability, examples; instability of differentiation, derivatives computation by difference formulas; the concept of extrapolation

Elements of numerical linear algebra:
vector and matrix norms, matrix and system conditioning; direct methods: Gaussian elimination and LU factorization, computation of inverse matrices, QR factorization, least-squares solution of overdetermined systems; iterative methods: Jacobi and Gauss-Seidel methods, general structure of stationary iterations

Laboratory: implementation and application of numerical codes in Matlab
Planned learning activities and teaching methods: Classroom lessons and laboratory exercises.

In particular, slides are used during the lectures, to simplify the lessons, and Matlab exercises are assigned, pointing out the relevant difficulties.
Additional notes about suggested reading: Suggested textbook and online teacher notes
(www.math.unipd.it/~alvise/didattica.html)
Textbooks (and optional supplementary readings)
  • A. Quarteroni et al., Introduzione al Calcolo Scientifico. --: Springer, 2016. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Laboratory
  • Interactive lecturing
  • Questioning
  • Problem solving

Innovative teaching methods: Software or applications used
  • Slides

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