First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063594, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
SC2095, Degree course structure A.Y. 2014/15, A.Y. 2017/18
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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
Other lecturers PAOLA MANNUCCI 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 02/10/2017
End of activities 19/01/2018
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
3 Commissione a.a. 2017/2018 01/10/2017 30/09/2018 TREU GIULIA (Presidente)
CESARONI ANNALISA (Membro Effettivo)
MANNUCCI PAOLA (Membro Effettivo)
PARMEGGIANI GEMMA (Membro Effettivo)

Prerequisites: The topics of the courses of Linear Algebra and Calculus 1.
Target skills and knowledge: We will deal with multivariate differential and integral calculus, sequences and series of functions, ordinary differential equations. The students will learn both the theoretical foundations and the practical skills that will let them to solve applicative problems.
Examination methods: Written examination.
Assessment criteria: Every question of each exercise contributes for a certain specified amount to the highest grade of 33/30 (corresponding to 30 cum laude).
The correctness, accuracy and completeness of the answers given to the different exercises are the criteria for the evaluation.
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: There will be 82 hours of lectures, at least one-third of them dedicated to numerical and theoretical exercises.
Additional notes about suggested reading: Mathematical Analysis. In the MOODLE page of Statistical Science, in the spase devoted to the course, there are the lecture notes, the exercises of past examinations and other staff. The theacher will provide the password to access to the theaching staff.
Textbooks (and optional supplementary readings)
  • P. Marcellini e C. Sbordone, Esercitazioni di Matematica, II vol. Parti prima e seconda. --: Liguori, --. Cerca nel catalogo
  • N. FUSCO, P. MARCELLINI, C. SBORDONE, Analisi due. --: Liguori, --. Cerca nel catalogo
  • Michiel Bertsch, Roberta Dal Passo, Lorenzo Giacomelli, Analisi Matematica. --: McGraw Hill, --. Cerca nel catalogo