Unit NUMERICAL ANALYSIS

Course
Mathematics
Study-unit Code
55999609
Curriculum
In all curricula
Teacher
Bruno Iannazzo
Teachers
  • Bruno Iannazzo
  • Ivan Gerace (Codocenza)
Hours
  • 42 ore - Bruno Iannazzo
  • 26 ore (Codocenza) - Ivan Gerace
CFU
9
Course Regulation
Coorte 2021
Offered
2023/24
Learning activities
Caratterizzante
Area
Formazione modellistico-applicativa
Academic discipline
MAT/08
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
Introduction to Numerical Analysis.
Fundamentals of Numerical Linear Algebra and Approximation Theory.
Reference texts
D. Bini, M. Capovani, O. Menchi, Metodi Numerici per l'Algebra Lineare, Zanichelli, Bologna, 1988.
R. Bevilacqua, D. Bini, M. Capovani, O. Menchi, Metodi Numerici, Zanichelli, Bologna, 1992.
J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer, 2002.
P. H. Davis, Interpolation and approximation, Dover, New York, 1975.
Material provided by the teacher (covering most of the arguments and provided at the begin of the course).
Educational objectives
It is the first course of numerical analysis and the main methods and concepts are introduced.
The student will know: the practical difficulties in dealing with continuous quantites using finite resources, the necessary techniques (mathematical theories and algorithms) to practically solve simple continuous problem; and the tools to evaluate the efficiency of a solution method.
Through simple modeling examples the student will understand the fundamentals of mathematical modeling.
Prerequisites
Polynomials. Linear Algebra. Differential calculus in several real variables. Basics of functional analysis (Hilbert spaces, Fourier series).
Teaching methods
Face-to-face lectures. Some seminars and numerical tests sessions.
Learning verification modality
Oral exams that consists in one exercise with different parts of growing difficulty and one question where some details of a topic are asked. The two parts have the same weight. The first one requires about one hour, the second about thirty minutes.
In the evaluation process the comprehension of the topic is priviledged with respect to the memorization.

The oral exam aims at evaluating the level of comprehension of the topics taught in the course and of the ability of use them.
Extended program
Introduction to Numerical Linear Algebra and Approximation Theory: computation of zeros of nonlinear functions; numerical solution of linear systems; polynomial interpolation; Hilbert space and uniform approximation; numerical quadrature; introduction to the numerical solution of ordinary differential equations.
Analysis and implementation of the treated algorithms and study of some mathematical models: applications.
Obiettivi Agenda 2030 per lo sviluppo sostenibile
4
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