Course Details for A.Y. 2018/2019

The information on this page refer to the academic year 2018/2019. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2018/2019

Name:

Geometria A / Geometry A

Type:

Course

Basic information

Code:

DT0018

Sector:

MAT/03

Credits:

: Bachelor Degree in Mathematics 12 CFU (a)

Term:

1^st semester

Degree(s):

Bachelor Degree in Mathematics 1^st anno curriculum Generale Compulsory

Language:

Italian

Teacher(s):

Maria Lucia Fania

Course Objectives

The goal of the course is to make the student familiar with the basic and more advanced linear algebra theory of linear algebra and with analytic geometry in the plane and in the 3-dimensional space. The student should also become acquainted with the problem of diagonalization of a matrix or their Jordan canonical form and also with quadratic forms and their canonical form. A particular family of plane curves is presented: the conics and their affine and metric classification. Also a particular family of surfaces is presented: the quadrics and their metric and affine classification.

Course Content

Matrices and systems of linear equations.
Vector spaces and change of bases.
Linear transformations and matrices associated to them.
Eigenvalues, eigenvectors and diagonalization.
Euclidean spaces. Inner product. Cross product. Orthogonal subspaces. Gram-Schmidt orthogonalization.
Affine and euclidean geometry.
Eigenvalues and eigenvectors of symmetric matrices. Spectral theorem.
Unitary and Hermitian matrices. Diagonalization of an hermitian matrix. Hermitian product.
Bilinear forms, quadratic forms and their canonical form.
Conics and their affine and metric classification. Quadrics and their affine and metric classification.
Isometries of euclidean spaces of dimension two and three.
Jordan canonical form of a matrix.

Assessment Methods and Criteria

Written and Oral Exam

Textbooks

Nicholson W.K. , Algebra lineare. Dalle applicazioni alla teoria , McGraw-Hill. ulteriore testo utile
Fania, M.L. , Appunti del corso di Geometria A, a.a. 2015/2016 testo di riferimento
Apostol T.M., Calcolo, volume secondo Geometria , Boringhieri. ulteriore testo utile
Campanella G., Esercizi di Algebra Lineare e Geometria , Aracne. ulteriore testo utile
Sernesi E. , Geometria 1 , Boringhieri . testo di riferimento
Flamini F., Verra A. , Matrici e Vettori. Corso di base di geometria e algebra lineare , Carocci . ulteriore testo utile

Notes

I Fisici mutuano i primi 9 CFU del corso, corrispondenti ai primi otto punti del programma.

Internet Resources

Homepage:

http://people.disim.univaq.it/~fania/didattica/didattica1819.html

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 21 gennaio 2019, 16:50