GEOMETRY AND ALGEBRA
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
INDUSTRIAL 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
SLAVICH LEONE (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 topics useful in other disciplines, with a great deal of motivation and many computational examples. A tutoring staff, composed by experienced graduate or undergraduate students, provides an expert help and support for students attending the course.
Course contents
Preliminaries
Polynomials and algebraic equations. Complex numbers and the Fundamental Theorem of Algebra.

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 Cramer theorems, 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.

Analitic Geometry
Coordinate systems in 2- and 3-dimensional spaces; straight lines and planes. Canonical forms of plane conics. Quadric surfaces.
Teaching methods
Lectures (hours/year in lecture theatre): 22.5
Practical class (hours/year in lecture theatre): 37.5
Practicals / Workshops (hours/year in lecture theatre): 0