Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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Mathematical Analysis 1

Professors:
Gilardi Gianni, Lisini Stefano
Year:
2015/2016
Course code:
500115
ECTS:
9
SSD:
MAT/05
DM:
270/04
Lessons:
84
Period:
I semester
Language:
Italian

Objectives

All the basic concepts of Mathematical analysis in several variables and calculus in one variable. Examples from applications to physics and ingeneering.

Teaching methods

Lectures at the blackboard.

Examination

Oral examination.

Prerequisites

Background given by the highschool.

Syllabus

Real and complex numbers.
Complex exponential and related functions.
Sequences and series of numbers or euclidean vectors.
Limits, continuity, differentiability and first order derivatives in several variables.
Tangent vectors and geometric viewpoint of differentiability.
Differentiation rules (jacobian matrix).
Implicit functions.
Maxima and minima in 1D.
Abstract measure and integration theory of Riemann type.
Calculus in 1D.
Divergence and curl in their integral forms (as limits).
Gauss and Stokes theorems (sketch).

Bibliography

G. Gilardi: "Analisi Matematica di Base", seconda edizione, McGraw-Hill, 2011.
Some material at http://www-dimat.unipv.it/gilardi/WEBGG/analisi1.htm

Modules

Professor:
Gilardi Gianni
Lessons:
54
ECTS:
6
SSD:
MAT/05

Professor:
Lisini Stefano
Lessons:
30
ECTS:
3
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