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

Provide tools for algebraic calculus and knowledge of analytical geometry of the plane and 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.

PREREQUISITES

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

TEACHING METHODS

As part of the innovation learning project adopted by the Bachelor Degree Course in Mechanical Engineering, novel tools will be used for the active learning of students. The goal is to increase students' skills via interactive, experience-based, learning methodologies (e-learning, teamwork, etc.) for enhanced student participation, using an advanced level of communication that makes the student more aware and autonomous.

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.

TEACHERS AND EXAM BOARD

Exam Board

ELEONORA ANNA ROMANO (President)

MATTEO VARBARO

VALENTINA BERTELLA (President Substitute)

ALESSIO CAMINATA (President Substitute)

FABIO TANTURRI (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8720/p/studenti-orario

Class schedule

GEOMETRY

EXAMS

EXAM DESCRIPTION

The examination consists of a mandatory written part and with the possibilty of an oral discussion. The written part is made up of some exercises and 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/three additional questions.

Exam schedule