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GEOMETRY

CODE 56720
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 8784 INGEGNERIA MECCANICA (L-9) - LA SPEZIA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/03
    LANGUAGE Italian
    TEACHING LOCATION
  • LA SPEZIA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    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 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 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

    Due to the COVID emergency, the lessons (52 hours) will be held remotely by the Teams software.

    The Team’s name is

    Lezioni di Geometria Ingegneria Meccanica - SP

    The code to connect is 25h19qy

    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.

     

    RECOMMENDED READING/BIBLIOGRAPHY

    • 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

    Exam Board

    MARIA VIRGINIA CATALISANO (President)

    VALENTINA BERTELLA

    SERGIO DE MICHELI

    DANILO PERCIVALE (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    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

    FURTHER INFORMATION

    Pre-requisites :

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