CODE  57069 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  2° Semester 
TEACHING MATERIALS  AULAWEB 
This introductory calculus course builds up on the mathematics learnt during the high school. The main topics of the course are differentiation and integration of functions of one variable.
The basic objective of Calculus is to relate smallscale (differential) quantities to largescale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Students should demonstrate an understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.
At the end of this course the students are expected:
Sets, equalities and inequalities, analytic geometry, trigonometry.
Both theory and exercises are presented by the teachers. Some tutorials will be carried out during the semester.
The real numbers  The real numbers, maxima, minima, supremum, infimum.
Functions  Elementary functions, composite function, inverse function.
Limits and continuity  Limits of functions. Continuity. Global properties of continuous functions. The intermediate value theorem and the extreme value theorem.
Differentiation  Derivative of a function. Tangent line. Derivative of the composite function and of the inverse function. The theorems of Rolle, Chauchy and Lagrange. De l’Hôpital's rule.
Integration  Riemann and Cauchy sums. Indefinite integral. Area of a planar region. Mean value theorem. Integral functions. The fundamental theorem of calculus. Calculating primitives.
Some notes and exercises are available.
Recommended books
Office hours: Upon appointment.
TOMMASO BRUNO (President)
FEDERICO BENVENUTO (President Substitute)
According to the accademic calendar
All class schedules are posted on the EasyAcademy portal.
The exam consists of two written tests:
The final mark of the exam is given by
(first part)*1/3 + (second part)*2/3
rounded up to the nearest whole number.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
Date  Time  Location  Type  Notes 

21/06/2023  09:00  GENOVA  Scritto  
12/07/2023  09:00  GENOVA  Scritto  
18/09/2023  09:00  GENOVA  Scritto  
08/01/2024  09:00  GENOVA  Scritto  
01/02/2024  09:00  GENOVA  Scritto 