2019_20
Educational guide 
Escola Tècnica Superior d'Arquitectura
A A A 
english 
Bachelor's Degree in Architecture (2010)
 Subjects
  MATHEMATICS II
   Contents
Topic Sub-topic
Conics: Detailed description of the conics, Chasles, Monge, general and reduced equation, calculation of elements: centers, vertices, axes, guidelines, focal circumferences, parameters, foci. Theorems relative to conics
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, classification according to own value 1.
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 scales: Classification of the displacements and scales of the Euclidean plane and Euclidean space, application to the generation of friezes and 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, curvature lines, Gauss curvature and mean curvature, isometries, Egregium theorem, ruled surfaces, strangulation line.