Mathematical analysis and Geometry (students M-Z)
annual course

Prof. Alessandra Rotunno









Syllabus (Learning aims)
The course aims at providing mathematical contents necessary for the learning of technical and scientific disciplines: Theory of Structures - Structural Engineering - Technical Physics. These contents are the basic elements of Mathematical Analysis, Linear Algebra and Analytical Geometry.
Course description
1. Vector spaces
_Structure of a vector space on a field
_Building an Euclidean space Sn; base of a vector space
_Operations between carriers; scalar products  
_Equations in a plane S3
2. Linear systems
_Definition of a linear system of m equations in n unknowns
_Definition of a matrix, sub-matrix, determinant and minor
_Sum and products of a matrix
_Matrix of coefficients and complete matrix
_Rouche-Capelli Theorem
_Discussion of linear systems
3. Analytical geometry
_From Euclid’s II postulate to the 1st degree equation
_Explicit line equation: angular coefficient and interception
_Equation of a straight line for two points and for one point with a given angular coefficient
_Equation of a straight line in homogeneous coordinates
_Parallelism and perpendicularity between straight lines
_Equation of a straight line in space
_Parametric equation of a straight line in a plane and in a space
_Parallelism and orthogonality between straight lines and planes
_Straight bands
4. Projection geometry elements
_Projection and section - perspective between lines: infinite point and improper point
_Prospect between planes: infinite straight line , improper straight line
_Representation of a straight line in a projective plane
5. Conics
_Space genesis and representation in the plane
_Conics in the Cartesian plane and projective plane
_Classification of the conics
Articulation of lessons
The course consists of lectures and tutorials. The exam consists of a written test and an oral test. At the end of the first half there is a "written elapsed test", reserved for those who regularly follow the classroom lessons. The final written exam for students who pass the "written elapsed test" is limited to the arguments in the second half.
P. Marcellini, C. Sbordone, Elementi di Calcolo, Liguori Editore.
P. Marcellini, C. Sbordone, Esercitazioni di matematica, I Volume (parte prima e parte seconda), Liguori Editore.
P. Marcellini, C. Sbordone, Esercitazioni di matematica, II Volume (parte prima e parte seconda), Liguori Editore.
N. Fusco, P. Marcellini, C. Sbordone Analisi matematica due, Liguori Editore.
Aldo G.S.Ventre, Matematica Due, Fridericiana Editrice Universitaria, 2011