OVERVIEW

The course provides an introduction to linear algebra and analytic geometry. In particular, it focuses on teaching algorithms to find the solutions of a system of linear equations, giving an overview of basic matrix theory, studying vector spaces and dealing with problems from analitic geometry in the plane and space.

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides an introduction to linear algebra and analytic geometry. In particular, it focuses on describing the solutions of a system of linear equations, basic matrix manipulations, an introduction to vector spaces and dealing with problems from analitic geometry over dimension 2 and 3.

AIMS AND LEARNING OUTCOMES

The first goal of the course is to learn how to solve systems of linear equations, making use of the theory of matrices. Inspired by physics, we will study further the geometry of vectors and their basic properties and operations. In particular, vectors will lead us to vector spaces and matrices to linear operators, making an entrance in the realm of linear algebra. In this course special attention will be paid to symmetric and orthonormal matrices, to the interconnection between linear operators and matrices, to diagonalization techniques and their applications to the geometry of vectors, conics and quadrics.

At the end of the course, the student will master the main algorithms in order to be able to tackle problems in linear algebra and analytic geometry.

PREREQUISITES

Basic knowledge of arithmetics, algebra, analysis, trigonometry and set theory.

TEACHING METHODS

The lectures will be taking place according to the rules established by CCS and the Ateneo. The main information will be given at the beginning and throughout the semester.

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the professor of the course  and with Professor Federico Scarpa (federico.scarpa@unige.it), the Polytechnic School - Engineering's disability liaison.

SYLLABUS/CONTENT

Basics on sets and functions. Complex numbers and polynomials. Systems of linear equations and Gauss' algorithm. Matrices, determinant and rank. Cartesian system of coordinates, points, lines and planes: cartesian and parametric equations, angles, distance, orthogonal projections. Free and applied vectors, their geometrical representation, scalar/cross product, their basic geometric properties and their significance. Vector spaces, subspaces, basis and dimension. Linear operators and the associated matrices (translations and rotations along the axis), base change (orthonormal). Eigenvalues, eigenvectors and diagonalization of matrices (symmetric and orthogonal) and their geometric significance. Quadratic forms, circles, spheres and conics.

RECOMMENDED READING/BIBLIOGRAPHY

• A. Bernardi, A. Gimigliano: Algebra Lineare e Geometria Analitica, Città Studi Edizioni
• E. Sernesi: Geometria vol. 1, Bollati-Boringhieri
• D. Gallarati: Appunti di Geometria, Di Stefano Editore-Genova
• M.R. Casali, C. Gagliardi, L. Grasselli: Geometria, Società Editrice Esculapio
• F. Odetti, M. Raimondo: Elementi di Algebra Lineare e Geometria Analitica, ECIG Universitas
• M. Abate: Algebra Lineare, McGraw-Hill
• L. Robbiano: Algebra lineare per tutti, Springer
• F. Bottacin: Esercizi di algebra lineare e geometria, Società Editrice Esculapio
• V. Bertella, A. Damiano: Esercizi su spazi vettoriali e applicazioni lineari, Società Editrice Esculapio
• L. Mauri, E. Schlesinger: Esercizi di algebra lineare e geometria, Zanichelli

TEACHERS AND EXAM BOARD

Exam Board

FRANCESCO VENEZIANO (President)

FABIO TANTURRI

MARIA ROSARIA PATI (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8715/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of the written and possible oral part. The written exam costists of solving exercises closely related to the main subjects of the course. The oral exam consists of answering questions, putting to light student's basic understanding and knowledge of the course.

ASSESSMENT METHODS

The written exam is intended to verify the student's capacity to solve problems, apply the main algorithms in the course, and show a good understanding of the main theoretical concepts developed during the semester, such as main theorems and definitions. The oral exam aims to verify the student's understanding of the basic concepts, definitions, and properties, seen during the course.

Exam schedule