First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INL1002610, A.A. 2019/20

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

Information on the course unit
Degree course 5 years single cycle degree in
IN0533, Degree course structure A.Y. 2010/11, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS 2
Department of reference Department of Civil, Environmental and Architectural Engineering
E-Learning website
Mandatory attendance
Language of instruction Italian
Single Course unit The Course unit CANNOT be attended under the option Single Course unit attendance
Optional Course unit The Course unit is available ONLY for students enrolled in BUILDING ENGINEERING AND ARCHITECTURE

Teacher in charge ANNAMARIA MAZZIA MAT/08

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/05 Mathematical Analysis 6.0

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

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 63 87.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2010 course timetable

Examination board
Board From To Members of the board
13 2019 01/10/2019 30/11/2020 MAZZIA ANNAMARIA (Presidente)
BERGAMASCHI LUCA (Membro Effettivo)
CIATTI PAOLO (Supplente)
12 2018 01/10/2018 30/11/2019 MAZZIA ANNAMARIA (Presidente)
BERGAMASCHI LUCA (Membro Effettivo)
CIATTI PAOLO (Supplente)

Prerequisites: Calculus 1 and euclidean geometry
Target skills and knowledge: The course aims to provide the basic notions of differential and integral calculus, with particular reference to two variables functions, to multiple integrals and to ordinary derivative functions.
Examination methods: Written examination.
A facultative test on MOODLE.
Assessment criteria: Understand the concepts and methods of Calculus.
Capacity of explain and solve problems of Calculus.
Course unit contents: Basis concepts of Mathematical Analysis II

Calculus for functions of several variables.

Topology. Limit and continuity. Partial derivatives. Higher derivatives. Differentiability. Directional derivative. Tangent plane. Chain rule. Taylor formula. Quadratic form. Maximum and minimum values. Implicit functions. Level curves. Constraints values.

Differential equations.

The Cauchy problem. Existence theorens. First order linear differential equations. Separable equations. Linear differential equations

Vector function. Curves and surfaces.

Vector functions. Derivatives of vector functions. Curves. Length curve. Jacobian transformation. Parametric surface. Tangent plane to a surface.

Multiple integrals.

Double integrals and properties. Change of variables. Triple integrals. Line integrals. Surface integrals. Center of mass. Rotation volume and surface.

Differential forms.

Linear differential form and their integral. Exact and closed forms.
Planned learning activities and teaching methods: The lectures are in classroom with the use of the dashboard.
Several exercises are made in classroom, other are made togheter with the students in order to verify the one's own knowledge.
Additional notes about suggested reading: Tutorial given by the professor on the MOODLE page.
Textbooks (and optional supplementary readings)
  • Hass, Joel; Thomas, George B.; Marcelli, Cristina, Analisi matematica 2equazioni differenziali e funzioni di piĆ¹ variabili. Edizione italiana a cura di: Cristina Marcelli. Milano: Torino, Pearson, 2014. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Working in group
  • Auto correcting quizzes or tests for periodic feedback or exams
  • Loading of files and pages (web pages, Moodle, ...)

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

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Quality Education