|
Type A
|
Code |
Competences Specific | | | A7 |
Knowledge of the analysis and theory of shapes and the laws of visual perception adapted and applied to architecture and urbanism. |
| | A13 |
Knowledge of number calculus, analytical and differential geometry and algebraic methods adapted and applied to architecture and urbanism. |
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Type B
|
Code |
Competences Transversal |
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Type C
|
Code |
Competences Nuclear |
|
Type A
|
Code |
Learning outcomes |
| | A7 |
Use of applied knowledge related to calculus, analytical and differential analysis and algebraic methods.
| | | A13 |
Use of applied knowledge related to calculus, analytical and differential analysis and algebraic methods.
|
|
Type B
|
Code |
Learning outcomes |
|
Type C
|
Code |
Learning outcomes |
| 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. |
| Methodologies :: Tests |
| |
Competences |
(*) Class hours
|
Hours outside the classroom
|
(**) Total hours |
| Introductory activities |
|
1 |
0 |
1 |
| Lecture |
|
29 |
37 |
66 |
| Problem solving, exercises in the classroom |
|
30 |
46 |
76 |
| Personal attention |
|
1 |
0 |
1 |
| |
| Extended-answer tests |
|
6 |
0 |
6 |
| |
(*) On e-learning, hours of virtual attendance of the teacher.
(**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies
| |
Description |
| Introductory activities |
The subject will be described and will be fixed how it will be organized. The Geometry that will be explained and used in the course will be commented. |
| Lecture |
The themery will be imparted masterfully on blackboard and when necessary, videocannon and computer will be used. |
| Problem solving, exercises in the classroom |
Problems and exercises will be solved in the ordinary classroom. |
| Personal attention |
Queries that students can make, face-to-face and individually, to the teacher in his office. |
|
Description |
|
Queries that students can make, face-to-face and individually, to the teacher in his office. It will be in
professor query schedule; the way to fix the time of the consultations
will be with the request directly to the professor in the schedule of
the classes or through his electronic mail. |
|
Methodologies |
Competences
|
Description |
Weight |
|
|
|
|
| Extended-answer tests |
|
Over the course, a continuous evaluation will be carried out consisting of three exams formed by various problems that will cover the course curriculum.
1st. exam 25% (conics and quadrics)
2nd. exam 25% (affine transformations)
3rd. exam 50% (all of the above, plus surfaces) |
100% |
| Others |
|
If the professor deems it appropriate, he will propose one or two practices with an added value, of one point each, on the overall course grade. |
|
| |
|
Other comments and second exam session |
|
In case of not approving the course with the continuous evaluation, the students will have a second call consisting of an exam, extended-answer tests, and 100% of the course grade will be evaluated. In the exams, which will be face-to-face, of both calls: no electronic devices will be used. |
| Basic |
Blas Herrera Gómez, Geometría para Arquitectura e Ingenierías. 3ª Edición., Ed. Blas Herrera, Tarragona, 2016
Blas Herrera Gómez, Problemas de Geometría. 4ª Edición., Ed. Blas Herrera, Tarragona, 2016
Blas Herrera Gómez, Cálculo y Álgebra, breves notas. 3ª Edición., Ed. Blas Herrera, Tarragona, 2015
|
|
| Complementary |
M.P. do Carmo, Differential geometry of curves and surfaces., Prentice-Hall, New Jersey 1976
J.M. Comis, Curvas y superficies en diseño de ingeniería., Servicio de publicaciones, U.P.V., Valencia, 1996
E. Hernández, Álgebra y geometría., Ed. Addison-Wesley Iberoamericana S.A, Wilmington, 1994
P. Puig Adam, Curso de geometría métrica., Ed. Euler S.A., Madrid, 1986
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| Subjects that it is recommended to have taken before |
|
(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation. |
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