First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
IN18101050, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
IN0515, Degree course structure A.Y. 2019/20, A.Y. 2019/20
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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
Department of reference Department of Industrial Engineering
Mandatory attendance No
Language of instruction Italian
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

Teacher in charge ALVISE SOMMARIVA MAT/08
Other lecturers EMMA PERRACCHIONE 000000000000

Course unit code Course unit name Teacher in charge Degree course code
IN18101050 NUMERICAL ANALYSIS (Numerosita' canale 3) ALVISE SOMMARIVA IN0506

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 of
Individual study
Lecture 9.0 72 153.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2019 course timetable

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
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
  • Problem based learning
  • Interactive lecturing
  • Working in group
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • One Note (digital ink)
  • Latex
  • Matlab
  • Slides and PDFs

Sustainable Development Goals (SDGs)
Quality Education Gender Equality