First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063594, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
SC2094, Degree course structure A.Y. 2014/15, A.Y. 2019/20
bring this page
with you
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS
Website of the academic structure
Department of reference Department of Statistical Sciences
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 GIULIA TREU MAT/05

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/05 Mathematical Analysis 9.0

Course unit organization
Period First semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 34 41.0 No turn
Lecture 6.0 48 102.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
3 Commissione a.a.2019/20 01/10/2019 30/09/2020 TREU GIULIA (Presidente)
CESARONI ANNALISA (Membro Effettivo)
PARMEGGIANI GEMMA (Membro Effettivo)

Prerequisites: Students are requested to know the topics covered by of the courses of Linear Algebra and Calculus 1.
Target skills and knowledge: Students will acquire the practical skills related to differential and integral calculus in several variables, to sequences and series of functions and to some types of ordinary differential equations.
Students will also acquire the theoretical foundations of the topics indicated above. This will allow them a methodologically rigorous use of the tools and will help to train their analytical and critical skills.
Examination methods: The acquired knowledge will be verified by a a written test. The test has to be completed in two hours and thirty minutes.
The test includes
1) two or three theoretical questions in which the students are asked to correctly report definitions, statements and some simple demonstrations of theorems presented in class;
2) a theoretical question asking the students to elaborate the basic concepts presented in the course;
3) three or four exercises in which it is asked to correctly apply, also from the methodological point of view, the tools presented in the course.
Assessment criteria: Each question of each exercise contributes for a certain specified amount to the maximum score of 33/30 (corresponding to 30 and honors).
The correctness, accuracy and completeness of the answers are criteria for a positive evaluation.
In particular, the knowledge of course topics, the acquisition of methodologies, the ability to apply the acquired tools and analytical skills will be evaluated.
Course unit contents: Sequences and series of functions. Pointwise and uniform convergence of sequences of real functions. The uniform limit of a sequence of continuous functions. Pointwise, uniform and total convergence of series of real functions. Power series, convergence radius. Taylor's series. Analitic functions. Differential calculus for real functions of n real variables. Basics of topology in the n-dimensional euclidean space. Open, closed, compact and connected sets. Limits. Algebra of limits. Continuity of a function at a point and in set. Continuity of composed fuction. Weierstrass theorem and connection theorem. Partial and directional derivatives. Higher order derivatives, Hessian matrix, Schwartz theorem. Differential of a function at a point. Chain rule. The problem of finding maxima and minima of a function. First order necessary condition for unconstrained problems. Sufficient conditions. Implicit function theorem. The problem of finding maxima and minima of a function: the case with constraints. Lagrange multipliers theorem. Lebesgue measure theory. The σ-algebra of Lebesgue measurable sets. Measurable and integrable functions. Definition of the integral of a function on a measurable set. Properties of the integral. Fubini-Tonelli's theorem (reduction formula) and the change of variables formula. Ordinary differential equations.
Planned learning activities and teaching methods: The entire course consists in 82 hours of lectures, at least one third of which is dedicated to exercises.
During the lessons some interactive activities are carried out, if the topics allow it. Such activities, for example, can consist in solving short exercises in pairs or in small groups.
Some online tests will be offered on a regular basis. Students can perform these tests to check their level of learning. Some questions will stimulate a deeper reflection on the topics of the course and will also encourage collaboration among the students.
Students may always ask clarification questions or ask the teacher to develope deeper the topics of the lecture.
Additional notes about suggested reading: During the first lesson the teacher will illustrate the reference texts in order to guide the students in the optimal use of them.
Lecture notes, exercises taken from previous examinations, other exercises and any other useful educational material will be uploaded in the Moodle platform of the Departement of Statistical Sciences.
Login to the Moodle platform requires a password that will be communicated by the teacher.
Textbooks (and optional supplementary readings)
  • P. Marcellini e C. Sbordone, Esercitazioni di Matematica, II vol. Parti prima e seconda. --: Liguori, --.
  • E. Acerbi, G. Buttazzo, Secondo corso di Analisi Matematica. --: Pitagora Editrice Bologna, --. Cerca nel catalogo
  • Bertsch, Michiel; Dal_Passo, Roberta, Analisi matematicaMichiel Bertsch, Roberta Dal Passo, Lorenzo Giacomelli. Milano: McGraw Hill, 2011.

Innovative teaching methods: Teaching and learning strategies
  • Interactive lecturing
  • Questioning
  • Auto correcting quizzes or tests for periodic feedback or exams
  • Active quizzes for Concept Verification Tests and class discussions
  • Video shooting made by the teacher/the students
  • Use of online videos
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Kaltura (desktop video shooting, file loading on MyMedia Unipd)
  • Latex
  • Mathematica

Sustainable Development Goals (SDGs)
Quality Education