|SCIENTIFIC DISCIPLINARY SECTOR||MAT/05|
Prerequisites (for future units)
The course is aimed at second year students who have acquired the fundamental knowledge related to the functions of one and two variables, to plane analytical geometry and linear algebra.
The course aims to provide the basics on Integration of functions of multiple variables, Integration on curves and surfaces, Vector fields. Provide algebraic calculation tools and knowledge of 3D analytical geometry
Students are expected to master the main techniques for calculating double and triple integrals, line integrals of scalar and vector fields, the basic properties of vector fields and the classical theorems of the differential calculus in Euclidean space (divergence, curl, Stokes, Gauss-Green).
At the end of the course students will be able to recall and present the theoretical notions that have been presnted during the lectures. Applying the various techniques introducted in the course and justifying every step, they will be able to:
The course aims at providing the necessary theoretical and operative knowledge for the understanding and solving of the problems in the following topics: change of coordinates in the 3-dimensional space, symmetric matrices and their signature, conics and quadrics, curves and surfaces from a differential point of view.
At the end of the course the student will be able to recall and present the theoretical notions she will have faced during the lectures. Moreover, by applying the algorithms and the solving technique introducted in the course and justifying every step, she will be able to:
- write down and analyse a change of coordinates in the 3-dimensional space given by a rotation and a translation;
- evaluate the signature and the positive/negative definition of a symmetric matrix;
- identify and study an assigned conic or quadric;
- study and characterise the geometry of a parametric curve or surface.
The student will have to know the tools for the calculation of double, triple, curvilinear and surface integrals and the fundamental properties of vector fields in view of the applications.
Differential calculus for functions of one and two variables. Integration of the functions of one variable. Plane analytic geometry, linear algebra.
Lectures and exercise sessions for about 60h (Mathematical Analysis) and 30h (Geometry), with teaching methods to be announced depending on the evolution of the pandemic situation.
The following topics will be dealt with from both a theorical and operative point of view, withouth a clear subdivision between lectures and exercise sessions.
Elements of linear algebra.
Change of coordinates, rotations and translations in the 3-dimensional space.
Quadratic forms and symmetric matrices.
Classification of conics and quadrics.
Differential geometry of parametric curves.
Differential geometry of parametric surfaces.
Canuto-Tabacco, Analisi Matematica II
Pagani-Salsa, Analisi Matematica 2
- A.Bernardi, A.Gimigliano, Algebra Lineare e Geometria Analitica, Città Studi Edizioni.
- M.V. Catalisano, A. Perelli, Appunti di geometria e calcolo numerico, Lectures notes available on the aulaweb page of the course
- M.E. Rossi, Algebra lineare, Lectures notes available on the aulaweb page of the course
- Silvio Greco, Paolo Valabrega – GEOMETRIA ANALITICA – Levrotto e Bella
- Silvana Abeasis - ALGEBRA LINEARE E GEOMETRIA - ZANICHELLI
- Marco Abate, Algebra Lineare , ed. McGraw-Hill
- E. Sernesi, Geometria vol 1, ed Bollati-Boringhieri
Office hours: Weekly office hours will be communicated. Meetings upon email requests will also be considered.
FILIPPO DE MARI CASARETO DAL VERME (President)
ELEONORA ANNA ROMANO
MATTEO SANTACESARIA (President Substitute)
FABIO TANTURRI (President Substitute)
All class schedules are posted on the EasyAcademy portal.
ANALYSIS: Written exam followed by an oral exam
GEOMETRY: Written exam followed by an oral exam
The written part will consist in the resolution of exercises on the topics of the teaching programme (see also the Aims and Learning Outcomes section). Through the resolution of the exercises the student will be evaluted in:
- her skills in identifying the theoretical and practical results which are necessary to approach and solve the problems, and general knowledge of the very same results;
- her skills in applying the suitable algorithms and procedures to solve the exercises;
- her skills in providing the right arguments and justifications for the involved steps she follows.
During the oral part the teacher will evaluated the student's knowledge which has not been positively emerged during the written part. At the same time, the teacher will evaluate her knowledge on the topics which have not been covered by the written part.
|20/12/2021||12:00||GENOVA||Scritto + Orale|
|18/01/2022||14:30||GENOVA||scritto di geometria|
|19/01/2022||09:00||GENOVA||Scritto + Orale|
|25/01/2022||09:00||GENOVA||orale di geometria|
|18/02/2022||09:00||GENOVA||Scritto + Orale|
|15/06/2022||09:00||GENOVA||Scritto + Orale|
|13/07/2022||09:00||GENOVA||Scritto + Orale|
|14/09/2022||09:00||GENOVA||Scritto + Orale|