GEOMETRY AND ALGEBRA
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
ELECTRONIC AND COMPUTER ENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (27/09/2021 - 21/01/2022)
ECTS
6
Lesson hours
60 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
BISI FULVIO (titolare) - 6 ECTS
Prerequisites
The same mathematics prerequisites for enrollment into the Engineering Faculty.
In particular, the following issues are required
elementary set theory;
basic algebra: monomials/polynomials, polynomial division, equations and
inequations (inequalities) of degree 1 or 2, also for fractions of polynomials;
functions;
basic trigonometry: goniometric functions, trigonometric equations and inequations,
double- and half-angle formulae etc., laws for right and oblique triangles;
Euclidean basic 2D and 3D geometry, including area and volume formulas for
mosto common figures, parallelism and orthogonality between straight lines and/or
planes, parallelograms.
Learning outcomes
This is a basic course on Linear Algebra and Analytic Geometry. Particular emphasis will be given to the fundamental concepts of Linear Algebra and Analytic Geometry as well as to the application of the latter to concrete numerical problems. A tutoring staff, composed by
support for students attending the course.
Course contents
Set and functions.
Linear Algebra
Vector spaces, vectors of R^n, linear subspaces; linear span of a set of vectors;
spanning sets and linear independence, basis, coordinates, and dimension.
Operations with matrices, determinant and rank of a matrix, inverse of a matrix.
Linear systems, Rouché-Capelli and Gauss elimination method,
representation of the set of the solutions of a linear system. Linear mappings
between vector spaces, kernel and image, matrix associated with a linear mapping.
Eigenvalues and eigenvectors of a linear operator, diagonalisation of a linear
operator. Inner product in R^n, orthonormal basis, Gram-Schmidt process.
Orthogonal matrices. Real quadratic forms. Spectral theorem: real symmetric
matrices and orthogonal diagonalisation.
Analytic Geometry. Coordinate systems in 2- and 3-dimensional spaces; straight lines and planes.
Teaching methods
Lectures and exercise sessions at the blackboard.