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Università degli Studi di Parma Università degli Studi di Parma
Second cycle degree course in
Management engineering
Università degli Studi di Parma
Department of Engineering for Industrial Systems and Technologies

GEOMETRY B
cod. 14003

borrowed from Corso di TIPO in CDS 3008 - GEOMETRIA - cod. 13102
Academic year 2010/11
2° year of course - First semester
Professor
Lucia ALESSANDRINI
Academic discipline
Geometria (MAT/03)
Field
A scelta dello studente
Type of training activity
Student's choice
24 hours
of face-to-face activities
3 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

We will study Linear Algebra and its applications, in particular to Geometry in the space.

Prerequisites

none

Course unit content

Linear Geometry in euclidean space. Vectors, length, distance, angle. Lines and planes in the space: description and their positions. Some quadric surfaces.
Vectors, matrices, linear systems. Vectors of the n-dimensional euclidean space and their operations. Scalar product, angle, orthogonality. Matrices: operations and properties. Determinants. Linear systems theory, the Gauss algorithm, the rank of a matrix. Rouché-Capelli Theorem.
Real and complex vector spaces.
Linear maps: kernel and image, the dimension's formula. Basis change and matrices. Matrices of linear maps on finite dimensional vector spaces.
Invariant subspaces, eigenvalues, eigenvectors. Diagonalization of operators. Orthogonal matrices and operators. Systems of ordinary differential equations with constant coefficients.
Bilinear forms and scalar products. Spectral theorem.

Full programme

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Bibliography

L. ALESSANDRINI, L. NICOLODI, GEOMETRIA A, ed. UNINOVA (PR)
L. ALESSANDRINI, GEOMETRIA B, ed. UNINOVA (PR)

Teaching methods

JOINT WRITTEN ORAL EXAM.

Assessment methods and criteria

written and oral examination

Other information

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2030 agenda goals for sustainable development

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