MATHEMATICAL ANALYSIS II
Academic year and teacher
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- Versione italiana
- Academic year
- 2021/2022
- Teacher
- ALESSIA ASCANELLI
- Credits
- 10
- Didactic period
- Primo Semestre
- SSD
- MAT/05
Training objectives
- The aim of the course is to knowledge and familiarity with calculus and analytic tools to work with functions of several real variable.
The main knowledge provided by the course will be:
series of functions, power series and Fourier series;
functions of several variables real valued and vector-valued: the concept of differentiability;
maxima and minima for functions of several variables;
measure to Lebesgue integral;
curves in n-dimensional space (in particular in in three dimensional space);
two dimensional surfaces in three-dimensional space:
the implicit function theorem and the inverse function theorem:
Lagrange multipliers theorem;
differential forms.
The main skills that students should acquire (that is to say, the abilities to apply their knowledge) will be:
to be able to study the convergence set of a power series;
to be able to study a several variable function ( if it is continuous, differentiable or class c-1);
to be able to calculate the length and the curvature of a curve;
to be able to calculate the area of a surface or its mean curvature;
to be able to prove if a differential form is exact or not. Prerequisites
- Differential and integral calculus (Riemann's theory) of functions of one real variable .
Course programme
- The course takes place in the first half and lasts 80 hours of lessons. About half of total class time is devoted to examples and exercises.
The course content:
series of functions, power series and Fourier series 818 hours);
functions of several variables real valued and vector-valued: the concept of differentiability,
maxima and minima for functions of several variables (8 hours);
measure to Lebesgue integral (18 hours);
curves in n-dimensional space (in particular in in three dimensional space)(8 hours);
two dimensional surfaces in three-dimensional space (10 hours);
the implicit function theorem and the inverse function theorem, Lagrange multipliers theorem (10 hours);
differential forms 8 hours). Didactic methods
- The course includes theoretical lectures, accompanied by blackboard exercises on all of the topics.
Learning assessment procedures
- Purpose of the examination tests is to check whether the students achieved an adequate level of the course educational goals or not, with respect to both the knowledge and the skills.
The examination consists of a written test, aimed to assess the student's ability to solve problems and exercises, and of an oral test, aimed at evaluating the theoretical knowledge.
The final grade of the examination is given by:
- one mark for the written test
- one mark of a oral test. Reference texts
- Nicola Fusco-Paolo Marcellini-Carlo Sbordone: Analisi Matematica due, Liguori Editore, Napoli, 1996.
Enrico Giusti: Analisi Matematica 2. Bollati Boringhieri, 2008
Carlo Domenico Pagani, Sandro Salsa: Analisi Matematica 2. Zanichelli, 2020
