2015/2016

2015/2016

DM270

MAT/03 (GEOMETRY)

DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

CIVIL AND ENVIRONMENTAL ENGINEERING

PERCORSO COMUNE

1°

1st semester (28/09/2015 - 15/01/2016)

6

55 lesson hours

ITALIAN

WRITTEN AND ORAL TEST

BONSANTE FRANCESCO (titolare) - 6 ECTS

The same mathematics prerequisites for enrollment into the Engineering Faculty.

The aim of this course is to give students the main notions and technical tools of elementary Linear Algebra and Euclidean geometry. The focus will be on the computational side and constructive applications will be given. We also provides some exercise classes (about 20-24 hours).

Preliminaries
Algebraic structures, polynomials, Cartesian coordinates.

Linear Algebra
Vector spaces: subspaces, linear dependence, basis and dimension Coordinates. Matrices: sum, product, determinant, rank, invertible matrices. Change of coordinates. Linear systems: Rouche' Capelli Theorem, Cramer rule, Gauss algorithm. Parametric systems. Linear applications: kernel, image, dimension Theorem. Matrix associated with a linear application. Linear operators: eingenvalues and eigenvector of a linear operator. Diagonalisation of a matrix. Matrix similarity. Scalar product: orthogonality, orthonormal basis, Grahm-Schmidt algorithm, orthogonal matrices. Symmetric matrices. Spectral Theorem for vector spaces of finite dimension. Quadratic forms: canonical form, sign of a quadratic form.

Euclidean geometry
Lines and planes: parametric equations and Cartesian equations. Orthogonal projections. Relative positions of two lines.

Lectures (hours/year in lecture theatre): 60
Practical class (hours/year in lecture theatre): 0
Practicals / Workshops (hours/year in lecture theatre): 0

Bisi, Bonsante, Brivio. Lezioni di algebra lineare con applicazioni alla Geometria analitica. Edizioni LaDotta. M.Grieco e B. Zucchetti. Algebra Lineare e Geometria Analitica. Ed. la Goliardica Pavese (1997).

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