- Docente: Antonella Grassi
- Credits: 6
- SSD: MATH-02/A
- Language: English
- Moduli: Antonella Grassi (Modulo 1) Sergio Venturini (Modulo 2)
- Teaching Mode: In-person learning (entirely or partially) (Modulo 1); In-person learning (entirely or partially) (Modulo 2)
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Statistical Sciences (cod. 6661)
Also valid for Second cycle degree programme (LM) in Statistical Sciences (cod. 6810)
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from Nov 09, 2026 to Nov 24, 2026
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from Nov 24, 2026 to Dec 15, 2026
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 instructors.
Teaching methods
Frontal lessons
Assessment methods
The examination consists of an oral examination.
The exam will verify the student's understanding both in terms of acquisition of concepts and methods, with application to concrete cases.
The use of Artificial Intelligence's tools is not allowed during the oral exam.
Teaching tools
Virtuale
Software maxima
Office hours on the web site of the Instructors.
Office hours
See the website of Antonella Grassi
See the website of Sergio Venturini
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.