


Politecnico di Torino  
Academic Year 2007/08  
03BCGBK Geometry 

1st degree and Bachelorlevel of the Bologna process in Automotive Engineering  Torino 





Objectives of the course
The student should be able to solve linear systems, formulate and solve problems of plane geometry, using vector methods and the
knowledge of simple plane figures. 
Prerequisites
Algebraic calculus and Euclidean geometry. Integer, rational, real numbers. Basic trigonometry.

Syllabus
Complex numbers: notations and foundamental operations.
Outlines on polynomials and algebraic equations. Plan vectors: opertaions, components, scalar product. Rn space and its operations. Vectorial subspaces. Dependence, independence, bases. Matrix and determinants. Operations between matrix and inverse matrix. Matrix rank, reduction. Linear systems. Systems solution using reduction. Analytical plan geometry: representation of a line, angles and distances, circumference. Polar coordinates. Outlines on conic sections and space analytical geometry (lines and plans). 
Laboratories and/or exercises
Practicals include development of exercises studied during lectures.
Mathematical concepts studied at the high school are revised. Didactic Material The reference texts are: GrecoValabrega: Lezioni di Geometria Volume I e II 100 pagine di Algebra lineare  100 esercizi di Algebra lineare ' 100 esercizi di geometria analitica piana Ed. Levrotto e Bella, Torino, 1977 Exam Procedure Written paper, followed by a short oral test. 
