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).
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
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