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 aims to provide the basic concepts of linear algebra and analytic geometry, with particular emphasis on matrix calculus, vector spaces, the solution of linear systems, and analytic geometry problems in 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

The course consists of 52 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions, theorems and some proofs, which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with examples and exercises. 

Attendance at lectures is strongly recommended.

Students with a certified SLD (Specific Learning Disorder), disability, or other special educational needs, as well as working students, are invited to contact the professor at the beginning of the course to agree on teaching and examination arrangements.

Students with disabilities or SLD who wish to request compensatory/dispensatory measures for the exam are also reminded that such a request must be sent, using the form at the following link https://modulionline.unige.it/richiesta-adattamenti#no-back , to the professor, to the DIME contact person (federico.scarpa@unige.it), and to the relevant office (inclusione.studenti@info.unige.it) at least 7 working days before the exam, in accordance with the guidelines available at https://unige.it/disabilita-dsa/richiesta-servizi

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

The teaching material, such as the Internal Lecture Notes (Perelli-Catalisano), will be available on the Team

"2026-27 Ing. MECCANICA Lezioni di Geometria", whose link and team code will be announced at the start of the course on Aulaweb.

The books listed below are suggested as supporting texts, but students may also use other Geometry textbooks for Engineering.

• 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

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/en/corsi/11976/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

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 unit.

The written exam serves exclusively to establish the minimum level of knowledge required for admission to the subsequent oral exam. Threshold for admission to the oral exam: correct and properly justified answers to three of the ten questions proposed.

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.

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule .