CODE 97166 2024/2025 9 cfu anno 1 INGEGNERIA GESTIONALE 10716 (L-9) - GENOVA MAT/05 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

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 integrals).

### 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 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. Separable first order differential equations, linear first order differential equations, linear second order differential equations with constant coefficients.

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).

## LESSONS

### LESSONS START

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

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## 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 this way, students are assessed on their knowledge and understanding of the content covered in the course, and on reasoning skills they have acquired.

### 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.