Università di Pavia - Offerta formativa

GEOMETRY AND ALGEBRA

Enrollment year

2020/2021

Academic year

2020/2021

Regulations

DM270

Academic discipline

MAT/03 (GEOMETRY)

Department

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

Course

ELECTRONIC AND COMPUTER ENGINEERING

Curriculum

PERCORSO COMUNE

Year of study

1°

Period

1st semester (28/09/2020 - 22/01/2021)

ECTS

6

Lesson hours

60 lesson hours

Language

Italian

Activity type

WRITTEN AND ORAL TEST

Teacher

BISI FULVIO (titolare) - 6 ECTS

Prerequisites

The same mathematics prerequisites for enrollment into the Engineering Faculty.

In particular, the following issues are required

elementary set theory;

basic algebra: monomials/polynomials, polynomial division, equations and

inequations (inequalities) of degree 1 or 2, also for fractions of polynomials;

functions;

basic trigonometry: goniometric functions, trigonometric equations and inequations,

double- and half-angle formulae etc., laws for right and oblique triangles;

Euclidean basic 2D and 3D geometry, including area and volume formulas for

mosto common figures, parallelism and orthogonality between straight lines and/or

planes, parallelograms.

In particular, the following issues are required

elementary set theory;

basic algebra: monomials/polynomials, polynomial division, equations and

inequations (inequalities) of degree 1 or 2, also for fractions of polynomials;

functions;

basic trigonometry: goniometric functions, trigonometric equations and inequations,

double- and half-angle formulae etc., laws for right and oblique triangles;

Euclidean basic 2D and 3D geometry, including area and volume formulas for

mosto common figures, parallelism and orthogonality between straight lines and/or

planes, parallelograms.

Learning outcomes

This is a basic course on Linear Algebra and Analytic Geometry. Particular emphasis will be given to the fundamental concepts of Linear Algebra and Analytic Geometry as well as to the application of the latter to concrete numerical problems. A tutoring staff, composed by

experienced graduate or undergraduate students, provides an expert help and

support for students attending the course.

experienced graduate or undergraduate students, provides an expert help and

support for students attending the course.

Course contents

Set and functions.

Linear Algebra

Vector spaces, vectors of R^n, linear subspaces; linear span of a set of vectors;

spanning sets and linear independence, basis, coordinates, and dimension.

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

Linear systems, RouchÃ©-Capelli and Gauss elimination method,

representation of the set of the solutions of a linear system. Linear mappings

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

Eigenvalues and eigenvectors of a linear operator, diagonalisation of a linear

operator. Inner product in R^n, orthonormal basis, Gram-Schmidt process.

Orthogonal matrices. Real quadratic forms. Spectral theorem: real symmetric

matrices and orthogonal diagonalisation.

Analytic Geometry. Coordinate systems in 2- and 3-dimensional spaces; straight lines and planes.

Linear Algebra

Vector spaces, vectors of R^n, linear subspaces; linear span of a set of vectors;

spanning sets and linear independence, basis, coordinates, and dimension.

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

Linear systems, RouchÃ©-Capelli and Gauss elimination method,

representation of the set of the solutions of a linear system. Linear mappings

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

Eigenvalues and eigenvectors of a linear operator, diagonalisation of a linear

operator. Inner product in R^n, orthonormal basis, Gram-Schmidt process.

Orthogonal matrices. Real quadratic forms. Spectral theorem: real symmetric

matrices and orthogonal diagonalisation.

Analytic Geometry. Coordinate systems in 2- and 3-dimensional spaces; straight lines and planes.

Teaching methods

Lectures and exercise sessions at the blackboard.

Reccomended or required readings

F.Bisi, F.Bonsante, S. Brivio. Lezioni di Algebra Lineare con Aplicazioni alla

Geometria Analitica. Edizioni La Dotta.

Geometria Analitica. Edizioni La Dotta.

Assessment methods

The final exam consists of two written and an oral test. The first written one deals with theory. The second written one deals with exercises. The oral test deals with both. Under certain specific conditions, the student can be

exonerated from oral test.

exonerated from oral test.

Further information

http://matematica.unipv.it/ghigi

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