### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
DANIELA LERA (Tit.)
Period
First Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2017]  PERCORSO COMUNE 12 96

### Objectives

KNOWLEDGE AND UNDERSTANDING.
The knowledge of the goal and guidelines of Numerical Analysis: well-posed and ill-conditioned problems, algorithms, errors, floating point systems, computational complexity, stability. Knowledge of the basic techniques for solving linear systems, approximation theory, nonlinear equations and differential equations.
APPLYING KNOWLEDGE AND UNDERSTANDING
The student, from the initial formulation of a numerical problem, must be able to find, if they exist, the numerical solutions and to evaluate the accuracy and the computational cost. In particular, the lessons with the Matlab are intended to develop the ability to identify the most suitable approach to the solution of the problems.
MAKING JUDGEMENTS
The course encourages students to work independently even in order to use alternative sources of information to educational material provided by the teacher. These sources can be other educational material available on the net, software, tutorials, interactive web of numerical analysis problems.
COMMUNICATION SKILLS
The course aims to achieve by the student not only the understanding of a subject, but also the exhibition capacity according to the formal rigor required by the Numerical Analysis. For this reason is provided a oral examination on some "key" topics of the course.
LEARNING SKILLS
The lectures were held so that they pass to elementary situations (definitions, theorems and methods) of immediate assimilation to complex situations.

### Prerequisites

A) Basic concepts of mathematical analysis: Sets. Functions of one or more variables. Continuity and derivability. Integration.
B) Basic knowledge of linear algebra. Vectors and Matrices. Determinant and rank. Linear Spaces. Finite and infinite spaces.

### Contents

Fundamental Notions. Linear spaces. Norms of vectors and matrices.
Floating point arithmetic and rounding errors.
Computer representation of numbers
Definitions and sources of error.
Well-posed computations.
Computational complexity
Systems of linear equations. Direct methods. Iterative methods.
Function approximation. Interpolation. Best Approximation.
Systems of nonlinear equations. Bisection method. Newton's method. Secant methods. Theory for one-point iteration methods.
Numerical solutions of ordinary differential equations.

### Teaching Methods

The tools used for the lectures will be both the blackboard and tablet with projection system via classroom screen.
The course, of 12 credits, consists of 96 hours of frontal lectures which, depending on the educational needs and the topics addressed, take place in the classroom with traditional teaching (blackboard, slide) or in a classroom equipped with appropriate hardware and software devices .
The frontal lectures on the blackboard will eventually be integrated by transparencies that will be made available to the student as teaching material on the teacher's website.
The student is enabled to then solve specific home-based exercises in the independent study.

### Verification of learning

The student will be evaluated on: acquisition of methods, knowledge of disciplinary language, ability to relate concepts and knowledge, exhibition capacity.
The exam consists of a written test followed by an oral. Passing the first is necessary to access the second one.
Written test
The written test consists of 18 questions, theoretical or exercises, covering all the topics discussed during the course. The written test is considered to be overcome if the vote is at least 18/30. The maximum test time is two hours.
Oral exam
The oral test consists of an interview during which the student must be able to expose the theoretical arguments and carry out the exercises. In particular it must be able to expose the algorithms studied and use Matlab language. The date of the oral examination is agreed with the teacher personally, by telephone or by email.
The final vote is determined by the vote of both tests:
18-23 the student has sufficient knowledge of the basic arguments of the course and is able to solve simple exercises.
24-27 the student has a good knowledge of all the arguments of the course and their Matlab-codes, as well as a good exhibition capacity.
28-30th the student has a perfect knowledge of the arguments of the course and of the Matlab programs, as well as a very good exhibition capacity.

### Texts

V.Comincioli, Analisi Numerica, metodi modelli applicazioni, McGraw-Hill Libri Italia, srl, Milano 1998.
A.Quarteroni, R. Sacco, F.Saleri: Matematica Numerica, Sprinter-Verlag 1998.
G.Rodriguez: Algoritmi Numerici, Pitagora Editrice, 2008.
J.Stoer, R. Burlisch, Introduzione all''Analisi Numerica, Ed. Zanichelli.
E.Isaacson, H.B.Keller, Analysis of Numerical Methods, John Wiley, New York.
F.Fontanella, A. Pasquali, Calcolo Numerico, Metodi ed Algoritmi, Ed. Pitagora, Bologna.
W.J Palm III, Matlab 6, Mc Graw-Hill.
W.H. Press et alii., Numerical Recipes, The art of Scientific Computing, Cambridge Press.