Lecturer: Marisa Grieco  

Course name: Geometria
Course code: 500116
Degree course: Ingegneria Edile-Architettura
Disciplinary field of science: MAT/03
L'insegnamento costituisce attività di base per: Ingegneria Edile-Architettura
University credits: CFU 6
Course website: n.d.

Specific course objectives

This is a base 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. Complex numbers.

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

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

Linear mappings:
Linear mapping 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 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, planes, and quadratic surfaces. Canonical forms of plane conics and quadratic surfaces.

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): 20
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

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

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 test, it is required a minimum grade in the written test.