Lecturer: Fulvio Bisi  

Course name: Linear Algebra
Course code: 500473
Degree course: Ingegneria Meccatronica, Ingegneria per l'Ambiente e il Territorio
Disciplinary field of science: MAT/03
University credits: CFU 6
Course website: http://smmm.unipv.it/teaching.html

Specific course objectives

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

Course programme

Preliminaries
Polynomials and algebraic equations. Complex numbers and the Fundamental Theorem of Algebra.

Vector spaces
Vector spaces, vectors of R^n, linear subspaces; linear span of a set of vectors; 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. Orthogonal matrices. Real quadratic forms. Spectral theorem: real symmetric matrices and orthogonal diagonalization.

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

Course entry requirements

The same mathematics prerequisites for enrollment into the Engineering Faculty. In particular: polynomial algebra; equations and inequalities; elementary trigonometry (basic trigonometric functions; basic trigonometric formulae; basic theorems for triangles); plane cartesian coordinates.

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

Suggested reading materials

B. Grieco, M. Zucchetti. Algebra Lineare e Geometria Analitica.. ed. La Goliardica Pavese (1997). .

Marco Abate, Chiara de Fabritiis. Geometria analitica con elementi di algebra lineare.. McGraw-Hill Italia (2006).

Testing and exams

The final exam consists of a written and an oral test. Both have to be passed within the same session. A minimum grade in the written test will be required to be admitted to the oral test.