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

The teaching aims to provide basic knowledge of linear algebra and analytical geometry, with particular attention to matrix calculus, vector spaces, the resolution of linear systems and analytical geometry problems in 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.

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. 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

LESSONS

LESSONS START

September 15, 2025

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. 

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.