Educational guide 2023_24 Escola Tècnica Superior d'Arquitectura

Contents

Topic	Sub-topic
Conics:	Detailed description of the conics, general and reduced equation, calculation of elements: centers, vertices, axes, guidelines, focal circumferences, parameters, foci. Theorems relative to conics, Chasles.
Quadrics:	Detailed description of quadrics, cyclic sections, generation with rules, general and reduced equation, calculation of elements: centers, vertices, axes, main planes, director planes, asymptotic cones, cyclic planes, parameters, umbilical points, strangulation line, directive conics, generatrix conics, generatrix lines. Theorems relative to quadrics.
Affinities:	Primary definitions, expression in coordinates, classification of remarkable affinities.
Orthogonal automorphisms:	Dual application, description of direct orthogonal automorphisms in the two-dimensional case, angle, description of the inverse orthogonal automorphisms in the two-dimensional case, classification of orthogonal automophisms in the three-dimensional case.
Displacements and similarities:	Classification of the displacements and similarities of the Euclidean plane and Euclidean space, application to the generation of mosaics.
Surfaces:	Differential application, first fundamental form, area, length and angle of curves on surfaces, Gauss and Weingarten applications, Meusnier and Euler theorems, points types according to the main curvatures, Gauss curvature and mean curvature, isometries, Egregium theorem, ruled surfaces, strangulation line.