Lecturer: Francesco Bonsante   Sonia Brivio  

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

Specific course objectives

This is a basic subject on Linear Algebra and Analytic Geometry. Emphasis is given to topics that will be useful in other disciplines with a great deal of motivation and many computational examples. A tutoring staff, by experienced undergraduate students, provides an expert help and support for students attending the course.

Course programme

Preliminaries:
Polynomials and algebraic equations.

Vector spaces:
Vector spaces, vectors of R^n, linear subspaces, spanning sets and linear independence, basis, coordinates, and dimension.

Matrices:
Operations with matrices, determinant and rank of a matrix, inverse of a matrix.

Linear mappings:
Linear mappings between vector spaces, kernel and image, matrix associated with a linear mapping.

Linear systems:
Linear systems, Rouche'-Capelli and Cramer theorems, Gauss elimination method, representation of the set of the solutions of a linear system.

Linear operators:
Eigenvalues and eigenvectors of a linear operator, diagonalization of a linear operator.

Inner product in R^n:
Inner product in R^n, orthonormal basis, Gram-Schmidt process. Real quadratic forms. Real symmetric matrices and orthogonal diagonalization.

Analytic Geometry:
Coordinate system in 3-dimensional space, lines and planes. Canonical forms of plane conics.

Course entry requirements

The same mathematics prerequisites for enrollment into the Engineering Faculty.

Course structure and teaching

Lectures (hours/year in lecture theatre): 30
Practical class (hours/year in lecture theatre): 30
Practicals / Workshops (hours/year in lecture theatre): 0
Project work (hours/year in lecture theatre): 0

Suggested reading materials

M.Grieco e B. Zucchetti. Algebra Lineare e Geometria Analitica. Ed. la Goliardica Pavese (1997).

M. Abate. Algebra Lineare. Ed. Mc Graw Hill (2000).

Testing and exams

The final exam consists of a written and an oral test. Both have to be passed within the same session. In order to be admitted to the oral text, it is required a minimum grade in the written test.