
Course unit
MATHEMATICAL ANALYSIS 1 (Ult. numero di matricola pari)
IN10100190, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/05 
Mathematical Analysis 
12.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
12.0 
96 
204.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
16 2018 canale 1 
01/10/2018 
15/03/2020 
CASARINO
VALENTINA
(Presidente)
CARAVENNA
LAURA
(Membro Effettivo)
ALBERTINI
FRANCESCA
(Supplente)
ROSSI
FRANCESCO
(Supplente)

15 2017 canale 2 
01/10/2017 
15/03/2019 
CARAVENNA
LAURA
(Presidente)
ALBERTINI
FRANCESCA
(Membro Effettivo)
CASARINO
VALENTINA
(Supplente)
MOTTA
MONICA
(Supplente)

14 2017 canale 1 
01/10/2017 
15/03/2019 
MOTTA
MONICA
(Presidente)
ALBERTINI
FRANCESCA
(Membro Effettivo)
CARAVENNA
LAURA
(Supplente)
CASARINO
VALENTINA
(Supplente)

Prerequisites:

It is useful to be familiar with the following topics:
polynomials,
algebraic expressions,
powers and logarithms,
analytic geometry (lines and conics, in particular),
trigonometry,
resolution of equations and inequalities,
systems of equations and inequalities. 
Target skills and knowledge:

The aim of the course is to become familiar with the main notions of differential and integral calculus.
At the end of the course, students should be able to appy some classical methods to compute limits of sequences and functions of a real variable, to study derivability and integrability of functions (also of several variables) and to study the summability of numerical series. 
Examination methods:

It is possible to take part in the exams only if students have previously booked online through Uniweb.
The exam consists of a written test and, in some cases, an oral test.
The written test is divided into two parts, with a single evaluation.
The first part consists of 2/3 theoretical questions (a definition, a statement of a theorem, a proof of a theorem).
The second part consists of 3 or 4 exercises of the type of those carried out in class or proposed during the course.
Books,mobiles, calculators are not allowed.
In some cases (when the written test is not completely satisfactory or when it is very well done) the teacher will ask to integrate the written test with an oral test.
Once the tests have been corrected, the results will be published and the names of the students who will have to take the oral exam will be published.
In order to pass the exam only with the written test or to be admitted to the oral exam, it is necessary to obtain a sufficient score in both tests. 
Assessment criteria:

The teacher will evaluate both knowledge and skills acquired by the student on the topics of the program. The examination will be considered satisfactory only if both final tests (theory and exercises) will be sufficient. An active participation during the lectures is strongly recommended. 
Course unit contents:

Elements of set theory. Numerical sets. Properties of functions of a real variable: injectivity, surjectivity, invertibility and monotony. Elementary functions. Maximum, minimum, supremum and infimum of sets. Limit of a sequence. Properties of bounded sequences and monotone sequences. Limit of a function. Continuous functions. Global properties of continuous functions. Properties of monotone functions. Derivatives: algebra of derivatives and geometric meaning of the derivative. Applications of the notion of derivability. Convexity of functions. Taylor's formula and asymptotic expressions of elementary functions. Growth order. Local comparison between functions. Study of the graph of a function. Numerical series. Indefinite integration of functions of a variable. Definition of primitive. Rules of integration and research of primitives. Definition of integral function. Definite integration of functions of a variable.
Fundamental theorem of integral calculus. Improper integrals.
Introduction to the real functions of several variables (notions of topology in the plane, continuity, derivability, directional derivability and differentiability). 
Planned learning activities and teaching methods:

The content of the course will be taught through lessons, typically on the blackboard.
In general, the teacher will provide the handwritten notes of the lessons on Moodle.
Weekly, exercises will be assigned, both entirely carried out and only proposed.
The teacher will meet the students weekly. In addition to this meeting,
students are encouraged to use a forum in moodle, to communicate with each other and with the teacher. 
Additional notes about suggested reading:

The course will concern classical mathematical topics.
Any book on which students are comfortable studying is welcome.
The (handwritten) notes of the lessons will be usually available on Moodle.
Examination samples from previous years will be available as well, from a certain moment on, through moodle.
The teacher will indicate during the course online platforms containing exercise and material adequate to the course.
Additional books
About the theoretical part:
Enrico Giusti, Analisi Matematica 1, Boringhieri.
About the exercises:
Esercitazioni di Analisi Matematica 1 , Marco Bramanti, Esculapio Editore (2011)
Esercizi di Analisi Matematica 1, Sandro Salsa, Annamaria Squellati, Zanichelli (2011). 
Textbooks (and optional supplementary readings) 

Marco Bramanti, Carlo D. Pagani e Sandro Salsa, Analisi matematica 1. Bologna: Zanichelli, 2008.

Innovative teaching methods: Teaching and learning strategies
 Flipped classroom
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex

