# GEOMETRY

_
iten
Code
56975
2020/2021
CREDITS
6 credits during the 1st year of 8721 Pleasure Craft Engineering (L-9) LA SPEZIA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/03
LANGUAGE
Italian
TEACHING LOCATION
LA SPEZIA (Pleasure Craft Engineering)
semester
1° Semester
modules
This unit is a module of:
Teaching materials

OVERVIEW

The course provides an introduction to linear algebra and analytic geometry, with particular focus on matrix computations, on vector spaces and on solving linear systems and analitical geometry problems in 2 and 3 dimensions.

Prerequisites: elementary knowledge of arithmetic, algebra, trigonometry, set theory.

## AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide the basic concepts of linear algebra and analytic geometry , particularly with respect to the matrix calculus , the vector spaces , to the solution of linear systems and problems of analytic geometry in space .

AIMS AND LEARNING OUTCOMES

Computation of expressions with complex numbers. Roots of a complex number.  Roots and factorization of polynomials. Calculations with matrices and linear maps. Solving systems of linear equations. Vector operations. Solving geometric problems by means of vectors, matrices, cartesian coordinates, and algebraic equations. Identification and canonical form of conics.

Teaching methods

Frontal Lectures (52 hours)

SYLLABUS/CONTENT

Sets and maps. Complex numbers and polynomials. Linear systems and gaussian elimination. Matrices, determinants, rank. Vector spaces. Vectors in geometry. Subspaces, bases, dimension. Linear maps. Matrices related to a linear map. Eigenvalues, eigenvectors. The diagonal form of a matrix. Quadratic forms. Systems of cartesian coordinates, linear changes of coordinates. Points, lines and planes: cartesian and parametric equations, parallelism, angles, distances, orthogonal projections. Circumferences and spheres. Conics.

• Lecture notes (Perelli-Catalisano) (see http://www.diptem.unige.it/catalisano/ )
• E.Carlini, M.V.Catalisano, F.Odetti, A.Oneto, M.E.Serpico, GEOMETRIA PER INGEGNERIA - Una raccolta di temi d'esame risolti, ProgettoLeonardo - Editore Esculapio (Bologna), 2011.
• S.Greco, P.Valabrega, Algebra lineare, Levrotto & Bella, 2009.
• S.Greco, P.Valabrega, Geometria analitica, Levrotto & Bella, 2009.
• Odetti-Raimondo – Elementi di algebra lineare e geometria analitica – ECIG, 2002.
• Web Resources: http://www.diptem.unige.it/catalisano/default.htm

## TEACHERS AND EXAM BOARD

Ricevimento: By appointment

Exam Board

DANILO PERCIVALE (President)

VALENTINA BERTELLA

MARIA VIRGINIA CATALISANO

## LESSONS

Teaching methods

Frontal Lectures (52 hours)

LESSONS START

The third week of September

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

GEOMETRY

## EXAMS

Exam description

The examination consists of a written part and an oral discussion. The written part is made up  of 10 questions that cover all the material of the course.

The use of notes, books, or electronic devices  is forbidden.

Assessment methods

The questions of the written part will verify both the operational skills through problem solving and the learning of the theory, such as definitions and theorems. During the oral test there will be a discussion about the written part and two to three additional questions.

Exam schedule

Date Time Location Type Notes
27/01/2021 09:00 LA SPEZIA Scritto + Orale
08/02/2021 14:30 GENOVA Scritto
09/06/2021 09:00 LA SPEZIA Scritto + Orale
09/06/2021 09:00 LA SPEZIA Scritto
30/06/2021 09:00 LA SPEZIA Scritto + Orale
09/07/2021 09:00 LA SPEZIA Scritto
08/09/2021 09:00 GENOVA Scritto
16/09/2021 09:00 LA SPEZIA Scritto + Orale

## FURTHER INFORMATION

Pre-requisites :

Elementary notions of arithmetic, algebra, trigonometry, set theory,