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## MATHEMATICAL ANALYSIS

CODE 97166 2022/2023 9 cfu during the 1st year of 10716 INGEGNERIA GESTIONALE (L-9) - GENOVA MAT/05 Italian GENOVA 1° Semester AULAWEB

## OVERVIEW

This is a semi-annual course, devoted to limits, differential calculus and integral calculus for functions of one real variable.

## AIMS AND CONTENT

### LEARNING OUTCOMES

Capability in following a line of logical reasoning; understanding of the essential properties of differential and integral calculus for functions of one variable and of numerical series. Acquisition of a sufficient calculation ability.

### AIMS AND LEARNING OUTCOMES

The main objective is to supply the fundamentals of differential and integral calculus in one variable. In particular, students are expected to develop the following skills: operations on limits and derivatives, study of functions of one variable, integral calculus (indefinite and definite and improper integrals), resolution of some specific differential equations.

### TEACHING METHODS

Lectures (90 hours), given in the mode that will be decided by the University of Genova. Moreover some tutorial exercitations will be carried out during the semester.

### SYLLABUS/CONTENT

Real numbers, cartesian coordinates in a plane, functions of one real variable, monotonic functions, composition and invertibility of functions, elementary functions, supremum and infimum, limits of functions, limits of sequences, infinitesimal and infinite functions, continuous functions and their properties, derivatives, derivation rules, derivatives of elementary functions, sign of derivatives in the study of monotonicity and convexity, maxima and minima, theorems of Fermat, Rolle, Lagrange, de l'Hopital, Taylor expansions and applications to critical points, definite and indefinite integrals, fundamental theorem of integral calculus, elements of differential equations.

### RECOMMENDED READING/BIBLIOGRAPHY

O. Caligaris, P. Oliva: Analisi matematica 1, ECIG (1990);

M. Bramanti, C. Pagani, S. Salsa: Analisi Matematica 1, Zanichelli (2008);

T. Zolezzi: Dispense di Analisi Matematica I, edizioni ERSU (anni 90);

P. Marcellini, C. Sbordone: Esercitazioni di matematica, Liguori (1988);

F. Buzzetti, E. Grassini Raffaglio, A. Vasconi: Esercizi di analisi matematica, Masson (1989);

M. Bertsch, R. Dal Passo: Elementi di analisi matematica, Aracne (2000).

M. Baronti, F. De Mari, R. Van der Putten, I. Venturi: Calculus problems, Springer (2016).

## TEACHERS AND EXAM BOARD

### Exam Board

LAURA BURLANDO (President)

MAURIZIO CHICCO

ADA ARUFFO (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/10716/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

The exam consists of a written and an oral test. Oral test has to be taken in the same exam appeal of written test.

Furthermore, during the semester, two partial written tests might be delivered.

### ASSESSMENT METHODS

The written examination consists in some exercises about the topics covered in this course. In such a test is proven the ability to solve problems relating to calculation of limits, derivatives and integrals of one variable functions, and study of properties of one variable functions.

The test lasts two hours and it is possible to consult the notes and textbooks.

In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding and the knowledge of the concepts and reasoning skills acquired by the students.

### Exam schedule

Date Time Location Type Notes
19/01/2023 14:00 GENOVA Scritto
26/01/2023 09:00 GENOVA Orale
10/02/2023 09:00 GENOVA Scritto
16/02/2023 09:00 GENOVA Orale
20/06/2023 09:00 GENOVA Scritto
26/06/2023 09:00 GENOVA Orale
13/07/2023 09:00 GENOVA Scritto
20/07/2023 09:00 GENOVA Orale
08/09/2023 09:00 GENOVA Scritto
14/09/2023 14:00 GENOVA Orale

### FURTHER INFORMATION

At the beginnng of the lectures, office hours for students will be established. Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.