- Docente: Sergio Venturini
- Credits: 6
- SSD: MAT/02
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Economics, Politics and Social Sciences (cod. 5819)
Also valid for Second cycle degree programme (LM) in Statistical Sciences (cod. 6810)
First cycle degree programme (L) in Statistical Sciences (cod. 8873)
Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)
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from Nov 10, 2025 to Dec 15, 2025
Learning outcomes
By the end of the course the student should know the basics of the mathematical analysis of multivariable functions. In particular the student should be able:- to perform multivariable differential calculus and compute partial derivatives - to identify maxima and minima for functions of several variables- to use constrained optimization: method of Lagrange multipliers- to compute multiple integrals
Course contents
Basic properties of the Euclidean space. Partial derivatives and differentiable functions. Critical points. Derivation of composite functions. Multivariate Taylor’s formula. Hessian matrices. Critical points analysis. Implicit functions: Dini’s theorem. Submanifold of the Euclidean space . Critical points on submanifolds.
Readings/Bibliography
Material provided by the teacher
Teaching methods
Frontal lessons
Assessment methods
The examination consists of an oral examination. Will occur 'the student's competency both in terms of acquisition of concepts and methods, with application to concrete cases.
Teaching tools
Software "maxima"
Office hours
See the website of Sergio Venturini