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 2020
- Offered
- 2022/23
- 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. - 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.