# GEOMETRY

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iten
Code
56719
2018/2019
CREDITS
6 credits during the 1st year of 8720 Mechanical Engineering (L-9) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/03
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Mechanical Engineering)
semester
1° Semester
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.

## AIMS AND CONTENT

LEARNING OUTCOMES

Purpose of the course is to provide algebraic computational tools and analytic geometric knowledges of two and three dimensional spaces.

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.

PREREQUISITES

Elementary knowledge of arithmetic, algebra, trigonometry, set theory.

Teaching methods

Frontal Lectures (60 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

MARIA VIRGINIA CATALISANO (President)

SERGIO DE MICHELI

## LESSONS

Teaching methods

Frontal Lectures (60 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.