CODE  57069 

ACADEMIC YEAR  2024/2025 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  2° Semester 
PREREQUISITES 
Propedeuticità in uscita
Questo insegnamento è propedeutico per gli insegnamenti:

TEACHING MATERIALS  AULAWEB 
OVERVIEW
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.
AIMS AND CONTENT
LEARNING OUTCOMES
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.
AIMS AND LEARNING OUTCOMES
At the end of this course the students are expected:
 to master the mathematical notation;
 to know the properties of the elementary functions and their graph;
 to be able to follow the mathematical arguments;
 and to solve simple exercises, and discuss the results obtained.
PREREQUISITES
Sets, equalities and inequalities, analytic geometry, trigonometry.
TEACHING METHODS
Both theory and exercises are presented by the teachers. Some tutorials will be carried out during the semester.
SYLLABUS/CONTENT
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.
RECOMMENDED READING/BIBLIOGRAPHY
Some notes and exercises are available.
Recommended books
 C. Canuto, A. Tabacco, Mathematical Analysis 1, ISBN: 9788891931115
 M. Oberguggenberger, A. Ostermann, Analysis for Computer Scientists: Foundations, Methods, and Algorithms, SpringerVerlag,
ISBN 9780857294456  M. Baronti, M., F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, SpringerVerlag, ISBN: 9783319154275
TEACHERS AND EXAM BOARD
Ricevimento: By appointment
Exam Board
GIOVANNI ALBERTI (President)
FEDERICO BENVENUTO (President)
LESSONS
LESSONS START
According to the accademic calendar
Class schedule
The timetable for this course is available here: Portale EasyAcademy
EXAMS
EXAM DESCRIPTION
The exam consists of one written test, composed of two parts:
 A test made of multiplechoice questions, about the theory seen during the course and with simple exercises
 Written test with more complex problems.
The exam is passed if both parts are sufficient. The final mark is given by
(first part)*1/3 + (second part)*2/3
ASSESSMENT METHODS
 The first part of the exam allows us to verify the ability of the students to handle the mathematical notation and to make simple deductive reasonings.
 The second part allows us to verify the ability to solve simple calculations and the knowledge of the main tools related to differentiation and integration.