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.
Purpose of the course is to provide algebraic computational tools and analytic geometric knowledges of two and three dimensional spaces.
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.
Elementary knowledge of arithmetic, algebra, trigonometry, set theory.
Due to the COVID emergency, the lessons (60 hours) will be held remotely by the Teams software.
The Team’s name is
Lezioni di Geometria Ingegneria Meccanica - GE
The code to connect is bqyttmg
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.
Web Resources:
http://www.diptem.unige.it/catalisano/default.htm
Ricevimento: By appointment
ELEONORA ANNA ROMANO (President)
MATTEO VARBARO
VALENTINA BERTELLA (President Substitute)
ALESSIO CAMINATA (President Substitute)
FABIO TANTURRI (President Substitute)
The third week of September.
GEOMETRY
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.
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.
