Course Details for A.Y. 2013/2014
Name:
Geometria A / Geometry A
Basic information
Credits:
: Laurea in Matematica 12 CFU (a)
Degree(s):
Laurea in Matematica 1° anno curriculum Generale Obbligatorio
Language:
Italian
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, metric and projective 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.
Projective space. Homogeneous coordinate. Projective classification of conics.
- Isometries of euclidean spaces of dimension two and three.
- Jordan canonical form of a matrix.
Assessment Methods and Criteria
Written and Oral Exam
Textbooks
- Chiantini L. , Algebra lineare e geometria analitica , Masson. ulteriore testo utile
- Nicholson W.K. , Algebra lineare. Dalle applicazioni alla teoria , McGraw-Hill. ulteriore testo utile
- 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.
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: 11 febbraio 2014, 08:48