First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
COMPUTER SCIENCE
Course unit
NUMERICAL ANALYSIS
SCP4063208, A.A. 2019/20

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

Information on the course unit
Degree course First cycle degree in
COMPUTER SCIENCE
SC1167, Degree course structure A.Y. 2011/12, A.Y. 2019/20
N0
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure http://informatica.scienze.unipd.it/2019/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 ANTONIA LARESE DE TETTO ICAR/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/08 Numerical Analysis 7.0

Course unit organization
Period Second 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 6.0 48 102.0 No turn

Calendar
Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Syllabus
Prerequisites: Basic knowledge of mathematical analysis and linear algebra.
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 laboratory exam.
Assessment criteria: The written exam aims at verifying the comprehension of the theoretical foundations of numerical methods.

The laboratory exam aims at verifying the implementation and application capabilities of numerical algorithms.
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; introduction to iterative methods.

Laboratory: implementation and application of numerical codes in Matlab.
Planned learning activities and teaching methods: Classroom lessons and laboratory exercises.
Additional notes about suggested reading: Suggested textbook and online teacher notes
(www.math.unipd.it/~marcov/studenti.html).
Textbooks (and optional supplementary readings)
  • A. Quarteroni et al., Introduzione al Calcolo Scientifico. --: Springer (una delle edizioni recenti), --. Cerca nel catalogo
  • A. Quarteroni et al., Scientific computing with Matlab and Octave. --: Springer, --. for foreign students Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Laboratory
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Latex
  • Matlab