Salta al contenuto principale della pagina

GEOMETRY

CODE 98169
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 10716 INGEGNERIA GESTIONALE (L-9) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/03
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course will provide the basic notions in linear algebra and analytic geometry necessary to any STEM student.

    AIMS AND CONTENT

    AIMS AND LEARNING OUTCOMES

    At the end of the course the student will be able to:

    - give correct definitions of the objects and properties studied, using the appropriate mathematical formalism;

    - recognize in concrete examples the geometrical objects and the algebraic properties studied;

    - describe the set of solutions of systems of linear equations;

    - solve exercises of plane and space geometry involving points, lines, planes, angles, distances, scalar products, orthogonal projections, conics, quadrics;

    - give explicit examples of objects that satisfy the geometrical or algebraic properties studied;

    - apply the notions and procedures studied in order to solve problems, also of new types and of an abstract nature.

     

    PREREQUISITES

    Basic arithmetic skills in computations and manipulations of algebriac formulas. Trigonometry.

    TEACHING METHODS

    Frontal lessons in class. Some exercises will be posted on Aulaweb. Attendance is strongly recommended.

    SYLLABUS/CONTENT

    Complex numbers: algebraic and trigonometric form. Solutions to z^n=a. Fundamental theorem of algebra.

    Polynomials: roots and multiple roots. Ruffini’s theorem. Factorization of polynomials in R[X].

    Algebraic operations on matrices. Invertibility of matrices.

    Gaussian elimination

    Determinant and rank of a matrix. Laplace expansion, Cramer theorem, Rouché-Capelli’s theorem.

    Vector spaces and linear maps.

    Diagonalization of endomorphisms. Eigenvalues and eigenvectors. Characteristic polynomial.

    Vector algebra in the plane and the space.

    Real symmetric matrices

    RECOMMENDED READING/BIBLIOGRAPHY

    The following notes will be posted on Aulaweb:
    1. Appunti di Geometria e Calcolo numerico (A. Perelli e M.V. Catalisano)
    2. Appunti di Algebra Lineare (M.E. Rossi).
    3. Appunti di Geometria (G. Niesi)
    Recommended book:  Algebra Lineare a Geometria Analitica (F. Odetti, M. Raimondo), ECIG Universitas.

    TEACHERS AND EXAM BOARD

    Exam Board

    FRANCESCO VENEZIANO (President)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    Exam schedule

    Date Time Location Type Notes
    01/06/2023 09:00 GENOVA Scritto
    06/06/2023 09:00 GENOVA Orale
    29/06/2023 09:00 GENOVA Scritto
    03/07/2023 09:00 GENOVA Orale
    11/09/2023 09:00 GENOVA Scritto
    13/09/2023 09:00 GENOVA Orale