Lecturer: Francesco Bonsante  

Course name: Geometria e algebra
Course code: 500473
Degree course: Ingegneria Civile e Ambientale
Disciplinary field of science: MAT/03
L'insegnamento costituisce attività di base per: Ingegneria Civile e Ambientale
University credits: ECTS 6
Course website: n.d.

Specific course objectives

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).

Course programme

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.

Course entry requirements

The same mathematics prerequisites for enrollment into the Engineering Faculty.

Course structure and teaching

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

Suggested reading materials

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).

Titolo del riferimento da modificare.

Testing and exams