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00013 - Mathematical Analysis

Academic Year 2021/2022

                
                        Docente:
                        Marco Mughetti
                    
                        Credits:
                        12
                    
                        SSD:
                        MAT/05
                    
                        Language:
                        Italian
                    
                        Moduli:
                        
                            Marco Mughetti
                            (Modulo 1)
                        
                            Daniele Morbidelli
                            (Modulo 2)
                        
                        Teaching Mode:
                        
                                    Traditional lectures (Modulo 1)
                                
                                    Traditional lectures (Modulo 2)
                                
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Computer Science (cod. 8009)

                            Teaching resources on Virtuale

Learning outcomes

At the end of the course, the student knows the basic tools of mathematical analysis such as real numbers, limits, continuity, derivatives and integrals. Moreover, he can use this tools for studying other disciplines

Course contents

The number sets: N,Z,Q,R.
The induction principle.
Sequences of real numbers.

Differential calculus for functions of one real variable.
Exponential and logarithmic functions. Trigonometric funtions.
Limits. Continuity (local and global properties).
Derivatives, monotony. Local maxima and local minima.
Infinite and infinitesimal asymptotics. Taylor's formula.

Integral calculus for functions of one real variable: primitive and integral, techniques of integration (by parts, by substitution), integral of rational functions. Generalized integrals.

An introduction to differential calculus for function of several variables. Continuity and derivatives for functions of several real variables.
Integral calculus for functions of two real variables.

Readings/Bibliography

Bertsch, Dal Passo, Giacomelli - Analisi matematica (McGraw-Hill)
Bramanti, Pagani, Salsa Matematica (Zanichelli)
Salsa, Squellati - Esercizi di Matematica I(Zanichelli)
Salsa, Squellati - Esercizi di Matematica II (Zanichelli)

Teaching methods

During the lectures, the teacher discusses the main topics of the theory, provides examples and shows how to solve several exercises.

Assessment methods

The exam aims to verify the reaching of the following didactical goals:

-knowledge of basic notions of mathematical analysis
-ability in using these notions in solving exercises and problems

The exam consists of two parts:

1) the first part consists of a set of exercises. Books, notes, computers and calculators are not allowed during this test.

2) the second part is focused on the theoretical aspects of the course. Only the students that have passed the first part are allowed to attend the second part.

Teaching tools

Blackboard, video and pc.

Virtual Class - Tutorato Prof. Chinni

Virtual Class

Office hours

See the website of Marco Mughetti

See the website of Daniele Morbidelli

SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.