The course is designed to provide the basic concepts and tools of linear algebra and analytic geometry. It is a first-semester, first-year course in which concepts that will be used in many subsequent courses are introduced.
The teaching unit is aimed at providing the basic concepts and tools of linear algebra and analytic geometry. It is a first semester course of the first year which introduces concepts that will be used in many subsequent courses.
The main goal of the course is to provide basic concepts of linear algebra and geometry, aiming at the development of a scientific approach to these topics and of the necessary tools to solve problems. Students are expected to gain the skills of understanding the text of a problem, look for solutions by means of the appropriate tools among the ones introduced in the course, solve the problem using appropriate arguments and express the results and conclusion in a clear and precise way.
Basic knowledge of arithmetics, algebra, analysis, trigonometry and set theory.
Lectures will be devoted to developing the theoretic part of the course, as well as to solving problems aimed to a better understanding of the theory. There will be additional hours devoted to discussion of exercises suggested by the lecturer.
Students having disabilities or Specific Learning Disorders can request suitable aids for the examinations. Such aids will be defined according to specific needs, together with the Referent for the Polytechnic School of the Committe for the inclusion of Students with Disabilites and with SLD. Students in such conditions are invited to get in touch (via e-mail) with the Teacher a sufficient time before the examination, inserting in copy the Referent for the Polytechninc School (https://unige.it/en/commissioni/comitatoperlinclusionedeglistudenticondisabilita.html), without sending any document about their disabilites.
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.
Material provided by the lecturer, available on the AulaWeb webpage of the course.
Ricevimento: Office hours by appointment via email
FABIO TANTURRI (President)
ARVID PEREGO
FRANCESCO VENEZIANO
VICTOR LOZOVANU (President Substitute)
In accordance with the manifesto. All class schedules are posted on the EasyAcademy portal.
Written test consisting of some exercises to be solved of the type seen during the course and possible oral test. Details will be communicated on Aulaweb.
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.
Ask the professor for other information not included in the teaching schedule.
