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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

GEOMETRY B
cod. 14003

borrowed from Corso di TIPO in CDS 3008 - GEOMETRIA - cod. 13102
Academic year 2009/10
2° year of course - First semester
Professor
Academic discipline
Geometria (MAT/03)
Field
A scelta dello studente
Type of training activity
Student's choice
36 hours
of face-to-face activities
4 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. <br />

Prerequisites

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Course unit content

<p> Linear Geometry in euclidean space. Vectors, length, distance, angle. Lines and planes in the space: description and their positions. Some quadric surfaces. <br />
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.</p>
<p>Real and complex vector spaces. <br />
Linear maps: kernel and image, the dimension's formula. Basis change and matrices. Matrices of linear maps on finite dimensional vector spaces. <br />
Invariant subspaces, eigenvalues, eigenvectors. Diagonalization of operators. Orthogonal matrices and operators. Systems of ordinary differential equations with constant coefficients. <br />
Bilinear forms and scalar products. Spectral theorem. </p>

Full programme

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Bibliography

<p>L. ALESSANDRINI, L. NICOLODI, GEOMETRIA A, ed. UNINOVA (PR)</p>
<p>L. ALESSANDRINI, GEOMETRIA B, ed. UNINOVA (PR)</p>

Teaching methods

JOINT WRITTEN ORAL EXAM.

Assessment methods and criteria

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Other information

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