CODE  97166 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  1° Semester 
TEACHING MATERIALS  AULAWEB 
This is a semiannual course, devoted to limits, differential calculus and integral calculus for functions of one real variable.
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.
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.
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.
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.
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).
Office hours: At the end of lectures or by appointment.
Office hours: At the end of lectures or by appointment.
LAURA BURLANDO (President)
MAURIZIO CHICCO
ADA ARUFFO (President Substitute)
All class schedules are posted on the EasyAcademy portal.
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.
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.
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 
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.