Mathematical Analysis 2
- Professors:
- Vitali Enrico
- Year:
- 2017/2018
- Course code:
- 500121
- ECTS:
- 9
- SSD:
- MAT/05
- DM:
- 270/04
- Lessons:
- 84
- Period:
- II semester
- Language:
- Italian
Objectives
The principal aim is to lead students to master the basic elements in those fields of Mathematical Analysis which are the natural continuation of the contents of the course {\it Mathematical Analysis 1.} In particular, the course deals with the main features and techniques from Analysis related to the study of functions beteween Euclidean spaces.
Teaching methods
Lectures at the blackboard.
Examination
Written and oral examination.
Prerequisites
Basic notions from the courses "Analisi Matematica 1" and "Algebra lineare".
Syllabus
Partial derivatives, differential, gradient and Jacobian matrix. Taylor formula and mean value theorem.
Convex functions. Maxima and minima with and without constraints. Invertible functions. Implicit functions.
Peano-Jordan measure, Riemann integral. Fubini's Theorem. Change of variables in multiple integrals.
Pointwise and uniform convergence. Series of functions. Power series and Taylor series.
Regular manifolds in Euclidean spaces. Integration on a manifold. Differential forms.
Convex functions. Maxima and minima with and without constraints. Invertible functions. Implicit functions.
Peano-Jordan measure, Riemann integral. Fubini's Theorem. Change of variables in multiple integrals.
Pointwise and uniform convergence. Series of functions. Power series and Taylor series.
Regular manifolds in Euclidean spaces. Integration on a manifold. Differential forms.
Bibliography
"Lezioni di analisi matematica" vol.2
di Giovanni Prodi (Boringhieri),
"Analisi matematica 2"
di Carlo D.~Pagani e Sandro Salsa (Zanichelli).
di Giovanni Prodi (Boringhieri),
"Analisi matematica 2"
di Carlo D.~Pagani e Sandro Salsa (Zanichelli).
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602