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## Subject: MATHEMATICAL ANALYSIS (A.A. 2022/2023)

### degree course in COMPUTER SCIENCE

Course year CFU 1 9 Unit Analisi matematica B12 (lesson) TAF: Basic compulsory subjects SSD: MAT/05 CFU: 9 Teachers: Michela ELEUTERI Moodle portal Aula virtuale su Microsoft Teams Verifica preparazione iniziale oral final vote Italiano

### Overview

Educational aims: (Dublin descriptors)

- knowledge and understanding: the aim of the course is to provide students with the basic tools of differential and integral calculus for functions of a real variable, with particular emphasis on the part of the Analysis related to natural numbers (induction principle, sequences, numerical series). At the end of the course the students will have to acquire the theoretical contents and the own methodologies of the Mathematical Analysis.

- application of knowledge and understanding - autonomy of judgment: at the end of the course students must know how to apply in a conscious way the concepts learned to solve problems of various kinds, even applied problems, based on mathematical models and should be able to identify the most appropriate methods to solve the proposed problems, motivating their choices.

- communication skills: students have to be able to communicate effectively and in a proper way, by showing logical-argumentative and synthesis skills.

Fractions, roots, powers, equations, inequalities, absolute value, logarithms, exponentials, trigonometric functions

These notions are absolutely FUNDAMENTAL in order to be able to follow the course. Beside the requirement of OFA to be overcome in order to be able to have access to the written parts of the course, starting from academic year 2019/2020 a new test has been required, named "prova prerequisiti": this consists in 4 questions (requiring an open answer, not a multiple choice to be done in 20 minutes) that are concerned with the following topics: fractions, roots, powers, equations, inequalities, absolute value, logarithms, exponentials, trigonometric functions. Each questions will be evaluated with maximum 2,5 points. To overcome the "prova prerequisiti" a student should get at least 8/10.
Along the academic year, the "prova prerequisiti" will be held separately from the other written tests while during the exams sessions it may be possibly part of it. If the "prova prerequisiti" will not be overcome, then the corresponding written test will not be evaluated.

### Course contents

Teaching takes place in the first semester of the first year for a total of 72 hours of frontal teaching corresponding to 9 CFU, of which usually about one third of numerical exercises. The scanning of the contents in terms of hours is to be understood as purely indicative. In fact, it may undergo changes during the course of teaching in light of the feedback and participation of students.
The first part of the course provides the basic knowledge of all that part of the Mathematical Analysis mainly linked to natural numbers: the induction principle, sequences and numerical series; in the second part of the course the general principles of differential and integral calculus for functions of a variable will be developed.
In details:
- 1 CFU - 8 hours of teaching
Prerequisites 2 hours
Natural numbers and induction principle 3 hours
Q and R fields 3 hours
- 1 CFU - 8 hours of teaching
Dedekind axiom 3 hours
Complex numbers 5 hours
- 1 CFU - 8 hours of teaching
Sequences of natural numbers 8 hours
- 1 CFU - 8 hours of teaching
Exercises concerning sequences of natural numbers 2 hours
Asymtotic notations 3 hours
Numerical series 3 hours
- 1 CFU - 8 hours of teaching
Exercises regarding numerical series 3 hours
Limits of functions of real variables 5 hours
- 1 CFU - 8 hours of teaching
Derivatives 5 hours
Approximation and Mac Laurin and Taylor expansions 3 hours
- 1 CFU - 8 hours of teaching
Continuous functions of a bounded interval: existence of zero theorem and Weierstrass theorem 2 hours
Fermat, Rolle, Lagrange, Cauchy theorems and their consequences 6 hours
- 1 CFU - 8 hours of teaching
Study of functions 5 hours
Riemann integral calculus for functions of one variable 3 hours
- 1 CFU - 8 hours of teaching
Integration methods 3 hours
Generalized integrals 5 hours

### Teaching methods

The lessons of the course will be provided in presence, accordingly with the guide lines provided from the University. In case of further restrictions connected with the pandemy, more details will be provided.

### Assessment methods

The assessment of learning is based on a written test and an oral exam. More details are given on the pdf file "Regole d'esame" present on the Dolly page of the course. In order to be able to have access to the written part of the test, a student should have overcome firse (in the following order) the OFA test and the "prova prerequisiti" test.

### Learning outcomes

- knowledge and understanding: at the end of the course students will have acquired the basic tools of differential and integral calculus for functions of a real variable, with particular emphasis on the part of the Analysis related to natural numbers (induction principle, sequences, numerical series). At the end of the course students will have acquired the theoretical contents and the own methodologies of the Mathematical Analysis.

- application of knowledge and understanding - autonomy of judgment: at the end of the course students will know how to apply in a conscious way the concepts learned to solve problems of various kinds, even applied problems, based on mathematical models and will be able to identify the most appropriate methods to solve the proposed problems, motivating their choices.

- communication skills: students will be able to communicate effectively and in a proper way, by showing logical-argumentative and synthesis skills.