IDENTIFYING DATA 2019_20
Subject (*) MATHEMATICS I Code 22204010
Study programme
Bachelor's Degree in Architecture (2010)
 Cycle 1st
Descriptors Credits Type Year Period
6 Basic Course First 1Q
Language
Castellà
Department Computer Engineering and Mathematics
Coordinator
FORTUNY ANGUERA, GERARD
 E-mail gerard.fortuny@urv.cat
Lecturers
FORTUNY ANGUERA, GERARD
Web
General description and relevant information Mathematics I aims to provide the student with the tools that will allow the systematic study of curves and surfaces in the plane and space. It is based on the students' previous mathematical knowledge and new tools are presented that will allow to properly formalize mathematical objects and entities which will have a deep study in Mathematics II.

Competences
Type A Code Competences Specific
 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
 A13 Integration of knowledge for solving questions using calculus and/or complex technical applications.
Type B Code Learning outcomes
 B2 Collect the information they need so that they can solve problems using data and not subjective opinion, and subjecting the information at their disposal to logical analysis.
Provide alternative solutions to a problem and evaluate risks and advantages.
 B6 Intervene effectively and convey relevant information.
Reply to the questions that they are asked.
Type C Code Learning outcomes
 C2 Use software for off-line communication: word processors, spreadsheets and digital presentations.
Use software for on-line communication: interactive tools (web, moodle, blogs, etc.), e-mail, forums, chat rooms, video conferences, collaborative work tools, etc.
 C4 Produce grammatically correct oral texts.
Produce well structured, clear and effective oral texts.
Produce oral texts that are appropriate to the communicative situation.

Contents
Topic Sub-topic
Numbers, successions and series. Presentation of different sets of numbers. Successions Series Taylor series.
Parametric equations and polar coordinates. Curves defined by parametric equations. Tangents and areas. Arc length. Polar coordinates. Areas and lengths in polar coordinates.
3D Functions Cylindrical and spherical coordinates. Functions Curves in space. Derivatives and integrals of vector functions.
Derivation of functions in several variables. Functions of several variables. Limits and continuity. Partial derivatives. Tangent planes and linear approximations. Chain rule. Directional derivatives. Gradient. Maximus and minimous. Lagrange multipliers.
Integration of functions in several variables. Double integrals over regions. Integration in polar coordinates. Area of a surface. Triple integrals. Change of variables in multiple integrals.
Differential equations. Definition and properties of differential equations. Linear differential equations of first and second order.
Vector spaces. Definition of vector space. Vector subspaces. Bases and base changes. Grassman formula.
Linear applications Definition of linear application. Core and image of a linear application. Matrix of a linear application.
Values and eigenvectors. Definition of vector and eigenvalue. Characteristic polynomial. Diagonalization theorem. Applications.

Planning
Methodologies  ::  Tests
  Competences (*) Class hours
 Hours outside the classroom
 (**) Total hours
Introductory activities
1 0 1
Lecture
A13
B2
B6
C2
C4
 29 37 66
Problem solving, exercises in the classroom
A13
B2
B6
C2
C4
 30 46 76
Personal attention
A13
B2
B6
C2
C4
 1 0 1
 
Extended-answer tests
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 It will be described what the subject consists of and how it is organized.
Lecture The syllabus will be taught masterfully on blackboard and when necessary, computer will be used.
Problem solving, exercises in the classroom We will solve the problems in the ordinary classroom, exercises and examples of exams with the problems that work in the concepts taught in the moments of the master version. The list of problems, exercises and exams can be found in the teacher's bibliography.
Personal attention It consists of attending to the questions that students deem appropriate to do to the teacher individually.

Personalized attention
Description
It consists of attending to the questions that students deem appropriate to do to the teacher individually. The way to fix the time of the consultations will be with the request of the same directly to the teacher in the schedule of the classes.

Assessment
Methodologies Competences Description Weight        
Extended-answer tests
A13
B2
B6
C2
C4
 During the course, continuous evaluation will be carried out consisting of three exams consisting of several problems that will include the course syllabus.

1st. Exam 25%
2nd. Exam 25%
3rd. Exam 50% 		100%
Others  

The bad personal attitude in class will count negatively. The demonstration in the class of mathematical knowledge will count in a positive way. Therefore, the total grade of the course can be modified based on the attitude and the demonstration in the classroom of good mathematical knowledge.

 
Other comments and second exam session

If they do not pass the subject with the continuous assessment, the students will have a second convocation consisting of a test, development test, and 100% of the course mark will be evaluated.

In the tests of both calls: no mobile phones or calculators will be used.

Sources of information

Basic Blas Herrera Gómez, Cálculo y Álgebra, breves notas. 2ª Edición., Ed. Blas Herrera, Tarragona 2013

Complementary J. Arvesú, F. Marcellán, J. Sanchez , Problemas Resuletos de Algebra , Ed. Thomson ,
B.P. Demidovich., Problemas y ejercicios de análisis matemàtico, Ed Paraninfo,
E. Hernández, Álgebra y geometría , Ed. Addison-Wesley Iberoamericana S.A,
R. Smith, R. Minton, Cálculo vol1., Ed. Mc Graw Hill,
T. Smith, B. Minton, Cálculo vol2. , Ed. Mc Graw Hill,
J. Stewart, Cálculo Multivariable , Ed. Thomson,

Recommendations

Subjects that continue the syllabus
MATHEMATICS II/22204009

Subjects that are recommended to be taken simultaneously
PHYSICS/22204007

(*)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.