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 Sistems

➢ 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 course

The course is annual, organized in lectures and tutorials for a total of 48 hours.

For each lesson will be published slides to be used as a clipboard for a theoretical and practical reference.

arguments in the second half.

 

For further information

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