Identifying Data 2020/21
Subject (*) Mathematics 2 Code 730G05005
Study programme
Grao en Enxeñaría Naval e Oceánica
Descriptors Cycle Period Year Type Credits
Graduate 2nd four-month period
 First Basic training 6
Language
Galician
Teaching method Hybrid
Prerequisites
Department Matemáticas
Coordinador
Brozos Vázquez, Miguel
 E-mail
miguel.brozos.vazquez@udc.es
Lecturers
Brozos Vázquez, Miguel
 E-mail
miguel.brozos.vazquez@udc.es
Web http://campusvirtual.udc.es/moodle
General description Esta materia comeza cunha introdución ao Cálculo diferencial e integral de funcións de varias variables. Posteriormente estúdanse curvas e superficies parametrizadas, vendo teoremas clásicos como o Teorema de Green para curvas e os Teoremas de Stokes e da Diverxencia para superficies.
Contingency plan 1. Modificacións nos contidos

Non se realizan cambios nos contidos.

2. Metodoloxías
*Metodoloxías docentes que se manteñen

As metodoloxías docentes mantéñense.

*Metodoloxías docentes que se modifican

Modifícase o carácter presencial polo non presencial e cámbiase o peso que terá a proba mixta e os traballos tutelados na avaliación.

3. Mecanismos de atención personalizada ao alumnado

Como mecanismos preferentes de atención personalizada utilizaranse os seguintes:
- Correo electrónico: aténdese diariamente.
- Moodle: aténdese diariamente, especialmente os foros de dúbidas e discusión que se crean en cada tema.
- Teams: utilízase para unha comunicación máis directa e úsase tanto en horario de titorías como solicitando unha cita para unha hora a convir.

4. Modificacións na avaliación

Fronte a un posible escenario de non presencialidade, gañarán peso na avaliación os traballos tutelados, que serán realizados polo alumnado e expostos por Teams ante o profesor da materia.
A proba mixta terá un peso inferior nun posible escenario de non presencialidade, que dependerá do momento do cuadrimestre no que este comece e a que contidos afecta máis directamente.

*Observacións de avaliación:

O alumnado con recoñecemento de dedicación a tempo parcial e dispensa académica de exención de asistencia ás clases avaliarase coa entrega de traballos e nas probas mixtas nas mesmas condicións que o resto do alumnado.
A avaliación na 2ª oportunidade seguirá os mesmos criterios que os da 1ª oportunidade.


5. Modificacións da bibliografía ou webgrafía

As fontes de información fundamentais estarán dispoñibles na plataforma Moodle da materia. Mantéñense as recomendacións bibliográficas pero favorecerase o uso de materiais dispoñibles na rede.

Study programme competencies
Code Study programme competences
A1 Skill for the resolution of the mathematical problems that can be formulated in the engineering. Aptitude for applying the knowledge on: linear algebra; geometry; differential geometry; differential and integral calculation; differential equations and in partial derivatives; numerical methods; algorithmic numerical; statistics and optimization
B1 That the students proved to have and to understand knowledge in an area of study what part of the base of the secondary education, and itself tends to find to a level that, although it leans in advanced text books, it includes also some aspects that knowledge implicates proceeding from the vanguard of its field of study
B2 That the students know how to apply its knowledge to its work or vocation in a professional way and possess the competences that tend to prove itself by the elaboration and defense of arguments and the resolution of problems in its area of study
B5 That the students developed those skills of learning necessary to start subsequent studies with a high degree of autonomy
B6 Be able to carrying out a critical analysis, evaluation and synthesis of new and complex ideas.
C4 Recognizing critically the knowledge, the technology and the available information to solve the problems that they must face.

Learning aims
Learning outcomes Study programme competences
Identify mathematical concepts and tools to solve problems that can appear in an engineering context. A1
 B1
B2
B5
B6
 C4
To show the ability of using techniques of Linear Algebra, Geometry and Calculus to be applied in problem solving. A1
 B1
B2
B5
B6
 C4

Contents
Topic Sub-topic
Sets and functions in R^n Scalar and vector functions.
Level sets.
Continuity.
Continuity in compact sets.
Differential Calculus Directional derivative. Partial derivative.
Differential of a function.
Gradient vector. Jacobian matrix.
Higher order derivatives. Introduction to vector calculus.
Taylor polynomial for scalar functions.
Critical points. Hessian matrix.
Conditional extreme values. Lagrange multipliers.
Integral Calculus. Double integrals.
Triple integrals.
Change of variables.
Applications to the computation of areas and volumes.
Differential Geometry Parameterized curves and line integrals.
Integrals of vector functions.
Gradient functions and conservative vector fields.
Green's theorem.
Parameterized surfaces.
Rotational and divergence.
Surface integrals.
Stokes theorem.
Divergence theorem.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A1 B5 B6 C4 30 30 60
Mixed objective/subjective test A1 B1 B2 B5 B6 C4 8 8 16
Supervised projects A1 B1 B2 B5 B6 C4 0 10 10
Problem solving A1 B1 B2 B5 B6 C4 30 30 60
 
Personalized attention 4 0 4
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Guest lecture / keynote speech Oral exhibition complemented with the use of audiovisual means and some questions headed to the students, with the purpose to transmit knowledges and facilitate the learning
Mixed objective/subjective test Written exam used for the evaluation of the learning, whose distinctive stroke is the possibility to determine if the answers given are or no correct. It constitutes an instrument of measure, elaborated rigorously, that allows to evaluate knowledges, capacities, skills, performance, aptitudes, attitudes, etc
Supervised projects Homework that professors are going to asses during the course.
Problem solving Technic by means of which one has to solve a specific problematic situation related to the contents of the subject.

Personalized attention
Methodologies
Supervised projects
Description
The contents of the subject as well as the developed methodologies require that students work by themselves. This will generate some questions that they can ask during the classes or during the office hours.


The students with recognition of part-time dedication and academic exemption from attendance can use the office hours as a reference in order to follow the course and the autonomous work.

Assessment
Methodologies Competencies Description Qualification
Mixed objective/subjective test A1 B1 B2 B5 B6 C4 Written exam will be used to assess learning of the contents of the subject. The exam consists of three parts, the first one will be performed during the course as a partial exam. This part will be eliminnatory and retrievable. The second part will be developed throughout the course by making homework and will be graded by assessing gained competences. The third part will be performed during the usual period of final exams and will assess the first, second and third parts. 80
Supervised projects A1 B1 B2 B5 B6 C4 Homework that professors are going to asses during the course. 20
 
Assessment comments

Students with recognition of part-time dedication and academic exemption
from attendance will be graded under the same conditions than other
students, as explained above.

The second opportunity will be based on the same criteria than the first one.

Sources of information
Basic Hwei P. Hsu (1987). Análisis Vectorial. Addison-Wesley
Marsden, J., Tromba, A. (2004). Cálculo Vectorial. Addison-Wesley
Larson, R., Hostetler, R., Edwards, B. (1999). Cálculo y Geometría Analítica, Vol. 2. McGraw-Hill
Salas, L., Hille, E.,Etgen, G. (2013). Calculus, vol I-II. Reverté
Gómez Bernúdez, C, Gómez Gratacos, F. (2018). Problemas de Cálculo. Andavira

Complementary

Resources from the webpage

http://maxima.sourceforge.net/

are recommended for dealing with Maxima software.

Recommendations
Subjects that it is recommended to have taken before
Mathematics 1/730G05001
Physics 1/730G05002

Subjects that are recommended to be taken simultaneously
Physics 2/730G05006

Subjects that continue the syllabus
Differential equations/730G05011

Other comments

Homework of this course will attend to the following:

              •  Preferably, virtual homework will be used, when printing is not required.

              •  In the case that paper is needed, then:

                 -     No plastic materials will be used.

                 -      Printing will be done both sides.

                 -      Recycled paper will be used as possible.

                 -      Unnecessary printed drafts will be avoided.

         In general, a sustainable use of natural resources will be done. Moreover, ethic principles related to sustainability will be followed.


(*)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.