First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
MATHEMATICAL ANALYSIS 1 (Ult. numero di matricola pari)
IN10100190, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
IN0509, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Number of ECTS credits allocated 12.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS 1
Department of reference Department of Management and Engineering
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge VALENTINA CASARINO MAT/05

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 12.0 96 204.0 No turn

Start of activities 23/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
18 2019 canale 2 01/10/2019 15/03/2021 ZOCCANTE SERGIO (Presidente)
17 2019 canale 1 01/10/2019 15/03/2021 CASARINO VALENTINA (Presidente)
ZOCCANTE SERGIO (Membro Effettivo)
16 2018 canale 1 01/10/2018 15/03/2020 CASARINO VALENTINA (Presidente)
CARAVENNA LAURA (Membro Effettivo)

Prerequisites: Real and rational numbers: elementary properties.
Algebra of polynomials. Absolute values of real numbers.
Basics on powers and logarithms.
Rational and irrational equations and inequalities.
Systems of equations and inequalities.
Lines, circles, ellipses, parabolas and hyperbolae in the Euclidean plane.
Basics on trigonometric functions (sinus, cosinus, tangent, cotangent),

Target skills and knowledge: The aim of this course consists in learning basic notions of Mathematical Analysis.
At the end of the course, a student should be able to consciously apply the classical methods of Mathematical Analysis both to compute limits of sequences and functions
and to solve derivability and integrability questions.
Examination methods: The exam will mostly consist in two parts, usually one just after the other:
1. Answering about three questions on the theoretical part of the course (usually, a definition, a statement of a theorem, a proof).
2. Solving about three or four problems.
During the semester there will be weekly assignments, which could help in the preparation of the final final written exam.
Assessment criteria: The final evaluation will take into account both the theoretical notions acquired during the course, and the competences in problem solving proved in the second part of the exam.
We strongly recommend an active participation in the lessons and in the office hours.
Course unit contents: Set theory. Number sets: Natural Numbers, Integers, Real Numbers.
Basics in Combinatorial Calculus. Maximum, minimum, infimum and supremum of number sets. Functions of one real variable: elementary functions, limits, continuity, monotonicity, invertibility.
Sequences of number, bounded sequences, monotone sequences. Limit of a sequence.
Differential calculus in one real variable, convexity and concavity. Taylor expansions with applications to limits and to compute derivatives. Local study of functions.
How to draw the graph of a function.
Number series. Convergence criteria.
Riemann integrals in one real variable: definite and indefinite integration.
Generalized integrals.
Introduction to calculus in several variables, various notions of differentiability.
Planned learning activities and teaching methods: Lectures, exercise classes, individual and/or group study and practice with weekly assignmenets, tutorial activities.
We also refer to the website, where past exam texts may be found.
Additional notes about suggested reading: Rough notes and exercises from lectures are available in Moodle almost daily or weekly during the course.
Any standard book on calculus could be used.
A library is also available close to classrooms.
Textbooks (and optional supplementary readings)
  • Bramanti, Marco; Salsa, Sandro, Analisi matematica 1. Bologna: Zanichelli, --. NON E' OBBLIGATORIO ACQUISTARE QUESTO LIBRO (vedi "Eventuali indicazioni sui materiali di studio"). Cerca nel catalogo
  • Bramanti, Marco, Esercitazioni di analisi matematica 1. Bologna: Esculapio, --. NON E' OBBLIGATORIO ACQUISTARE QUESTO LIBRO (vedi "Eventuali indicazioni sui materiali di studio"). Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Problem solving
  • Flipped classroom
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex