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GEOMETRY

CODE 56716
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 10375 INGEGNERIA CHIMICA E DI PROCESSO (L-9) - GENOVA
  • 6 cfu during the 1st year of 8716 INGEGNERIA ELETTRICA (L-9) - GENOVA
  • 6 cfu during the 1st year of 8715 INGEGNERIA CIVILE E AMBIENTALE (L-7) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/03
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    PREREQUISITES
    Prerequisites (for future units)
    This unit is a prerequisite for:
    • Electrical Engineering 8716 (coorte 2022/2023)
    • MATHEMATICAL ANALYSIS II 60243
    • POWER GENERATION 60221
    • FOUNDATIONS OF ELECTRICAL ENGINEERING 60334
    • MATHEMATICAL PHYSICS 1 60352
    • APPLIED PHYSICS 60359
    • MECHANICS OF MACHINES 86899
    • SOLID AND MACHINE MECHANICS 80338
    • ELECTRIC AND MAGNETIC FIELDS 60335
    • CIRCUIT THEORY 60336
    • STRUCTURAL MECHANICS 66283
    • ELECTRONICS FOR ELECTRICAL ENGINEERING 84372
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The student must learn the concept of number of solutions of a mathematical problem, must know how to work with complex numbers vectors and matrices, including their diagonalization, must be able to solve equations and linear systems, must know how to make a change of coordinates in the plane and in space, as well as knowing how to solve simple problems concerning lines, planes, spheres, circles and conic sections

    AIMS AND LEARNING OUTCOMES

    Complex numbers and representation in the Gauss plane: powers and solution of particular equations.

    Real / complex coefficient polynomials: factor breakdown, fundamental theorem of Algebra and Ruffini's theorem.

    Geometric vectors: equivalence, module, versorem operations and properties. Scalar and vottorial product and property. Mixed product of carriers.

    Linear systems: elementary operations on equations and Gauss theorem-algorithm

    Matrices: various definitions, operations and properties. Reverse matrix. Definition of characteristic and Rouchè Capelli Theorem with method for determining the solutions of a linear system. Determinant definitions e

    Finitely generated vector spaces: basic definitions of size and relative theorems, subspaces.

    Definition of linear application.

    Changes of coordinates in the plane and in space, formulas of rotations and translations. Orthogonal matrices.

    Matrix diagonalization: definition of eigenvalue, eigenvector and relative theorems. Spectral theorem for symmetric matrices.

     Lines in the plane and lines and planes in space: parametric and Cartesian equations. Various formulas of analytic geometry.

    Spheres and circumferences in space.

    Quadratic forms and Conic sectionss: associated matrices and defining character.

     Conic sections classification:   parabolic, elliptic and hyperbolic type (canonical equations and theorems on canonical form reduction.

    PREREQUISITES

    Algebra: factor decomposition: binomial and trinomial square, equation and inequalities of first, second degree and fractional.

    Trigonometry: definitions of the sine, cosine, tangent, their graphical representations and main formulas.

    Euclidean geometry: similitudes and equality of triangles, theorems of Pythagoras and Euclid, circles.

    TEACHING METHODS

    The course (four-months) consists of 3 hours of theory + 2 hours of exercises a week for 12 weeks.

    There are also two optional afternoon hours of guided exercises in the presence of tutors and lecturers.

     

    RECOMMENDED READING/BIBLIOGRAPHY

    Notes and exercises can be found on the website AulaWeb of the web classroom

    Suggested book:

    Odetti-Raimondo Elementi di Algebra lineare e geometria analitica   (ECIG)

    TEACHERS AND EXAM BOARD

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    The exam consists of a written test and an oral test.

     

    ASSESSMENT METHODS

     Knowledge of the statements and demonstrations of the most important theorems is required, as well as the ability to use these tools in a critical way, also for the resolution of new problems for the student.

    Exam schedule

    Date Time Location Type Notes