IDENTIFYING DATA 2019_20
Subject (*) MATHEMATICS II Code 22204009
Study programme
Bachelor's Degree in Architecture (2010)
 Cycle 1st
Descriptors Credits Type Year Period
6 Basic Course First
Language
Castellà
Department Computer Engineering and Mathematics
Coordinator
HERRERA GÓMEZ, BLAS
 E-mail blas.herrera@urv.cat
Lecturers
HERRERA GÓMEZ, BLAS
Web http://deim.urv.cat/~bherrera
General description and relevant information The course consists of the mastery of the geometry of the conics and quadrics, as well as the affinities, movements, similarities and projections in three-dimensional Euclidean space. Likewise, it consists of knowing the basic elements of the theory of curves, surfaces. All with the idea of being useful in the art and science of Architecture.

Competences
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.
Type B Code Competences Transversal
 B2 Resoldre problemes complexos de forma efectiva en el camp de l'Arquitectura.
 B6 Clear and effective communication of information, ideas, problems and solutions in public or a specific technical field
Type C Code Competences Nuclear
 C2 Be advanced users of the information and communication technologies
 C4 Be able to express themselves correctly both orally and in writing in one of the two official languages of the URV

Learning outcomes
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
 B2 Identify problems and take decisions to solve them.
Provide alternative solutions to a problem and evaluate risks and advantages.
 B6 Structure their presentations and comply with any requirements should there be any.
Reply to the questions that they are asked.
Type C Code Learning outcomes
 C2 Understand basic computer hardware.
Understand the operating system as a hardware manager and the software as a working tool.
 C4 Produce grammatically correct written texts
Produce well-structured, clear and rich written texts
Produce written texts that are appropriate to the communicative situation

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.

Planning
Methodologies  ::  Tests
  Competences (*) Class hours
 Hours outside the classroom
 (**) Total hours
Introductory activities
1 0 1
Lecture
A7
A13
B2
B6
C2
C4
 29 37 66
Problem solving, exercises in the classroom
A7
A13
B2
B6
C2
C4
 30 46 76
Personal attention
A7
A13
B2
B6
C2
C4
 1 0 1
 
Extended-answer tests
A7
A13
B2
B6
C2
C4
 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
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 topics related to the conics and quadrics will be taught, in the masterful explanation, with computer and video cannon, and will show the relevant drawings in class. The rest of the syllabus will be imparted masterfully on blackboard and when necessary, video cannon and computer will be used.
Problem solving, exercises in the classroom Problems, exercises and examples of exams will be solved in the ordinary classroom; with they, the concepts taught in the masterful explanation will be worked on. The list of such problems, exercises and exams, and even the solution of them, can be obtained in the professor's bibliography.
Personal attention It consists of attending, to the questions that students deem appropriate to make to the teacher, individually.

Personalized attention
Description
It consists of attending, to the questions that students deem appropriate to make to the teacher, individually. 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: blas.herrera@urv.cat.

Assessment
Methodologies Competences Description Weight        
Extended-answer tests
A7
A13
B2
B6
C2
C4
 Throughout the course a continuous assessment will be carried out consisting of three exams formed by several problems that will cover the course syllabus.

1st. exam 25%
2nd. exam 25%
3rd. exam 50% 		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 of both calls: mobile phones and calculators will not be used.

Sources of information

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

Recommendations


Subjects that it is recommended to have taken before
MATHEMATICS I/22204010
(*)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.