
Course unit
MATHEMATICAL ANALYSIS 2
INL1002610, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Lecture 
6.0 
63 
87.0 
No turn 
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.

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
Sustainable Development Goals (SDGs)

