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### Mathematical Analysis 2

Professors:
Gilardi Gianni, Lisini Stefano
Year:
2015/2016
Course code:
500121
ECTS:
9
SSD:
MAT/05
DM:
270/04
Lessons:
84
Period:
II semester
Language:
Italian

#### Objectives

Development of the subjects given in Mathematical Analysis 1: higher order derivatives, more on several variables. ODEs, complements. Sequences and series of functions. Linear differential forms.

#### Teaching methods

Lectures at the blackboard.

#### Examination

Oral examination.

#### Prerequisites

Basics on Mathematical Analysis and Linear Algebra.

#### Syllabus

Global properties of continuous functions: maxima and minima, uniform continuity and applications (e.g., to integration theory).

Mean value theorems and their applications to functions of one or several variables (e.g., use of the sign of the derivatives, Taylor expansion, De L'Hopital's rule; differentiation of integrals depending on parameters; study of stationary points and convex functions in several variables, Lagrange multipliers).

Integral calculus in several variables (multiple, line and surface integrals; change of variables).

Basics on ODEs and systems (Cauchy problem, global and local solutions).
The easiest and basic elements on linear ODEs.

Uniform convergence and applications.
Power series in 1D.

Exact and closed linear differential forms in several variables.

#### Bibliography

G. Gilardi: "Analisi Matematica di Base", seconda edizione, McGraw-Hill, 2011.
Some material at http://www-dimat.unipv.it/gilardi/WEBGG/analisi2.htm

#### Modules

Professor:
Gilardi Gianni
Lessons:
60
ECTS:
7
SSD:
MAT/05

Professor:
Lisini Stefano
Lessons:
24
ECTS:
2
SSD:
MAT/05

Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602