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
The course will give to the students basic tools of linear algebra and analytic geometry. A goal of the course is to train the student to follow logical deductive arguments, and to use the proper formal language. The student will learn to solve some linear algebra problems, that generally occur as intermediate steps in the solution of more complex mathematical models for engineering problems
Elementary knowledge of arithmetic, algebra, trigonometry, set theory.
Frontal Lectures (52 hours)
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.
Web site:
http://www.diptem.unige.it/catalisano/default.htm
Ricevimento: By appointment, via e-mail: mariavirginia.catalisano@unige.it
MARIA VIRGINIA CATALISANO (President)
SERGIO DE MICHELI
VALENTINA BERTELLA (President Substitute)
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.
