Identifying Data 2019/20
Subject (*) Mathematics II Code 631G02156
Study programme
Grao en Tecnoloxías Mariñas
Descriptors Cycle Period Year Type Credits
Graduate 2nd four-month period
 First Basic training 6
Language
Spanish
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Cao Rial, María Teresa
 E-mail
teresa.cao@udc.es
Lecturers
Cao Rial, María Teresa
Rodriguez Aros, Angel Daniel
 E-mail
teresa.cao@udc.es
angel.aros@udc.es
Web http://www.nauticaymaquinas.es/
General description Nesta materia vanse estudar os Lugares Xeométricos no plano e no espazo tridimensional (con especial énfase nas cónicas e cuádricas), Análise de Funcións Reais de Varias Variables Reais e Ecuacións Diferenciais.
O alumno tamén vai a mellorar as súas habilidades na aprendizaxe e desenvolvemento de novos métodos e tecnoloxías necesarias para continuar a súa formación. Tamén a traballar con material bibliográfico e recursos informáticos, a elaborar unha memoria/informe de modo rigoroso e sistemático, a escribir e transmitir coñecementos correctamente, a realizar eficazmente as tarefas asignadas como parte dun grupo, etc. En concreto será capaz de resolver e analizar os resultados dos problemas matemáticos que poidan xurdir na enxeñería, a usar modelos matemáticos e a identificar o caso en que deben aplicarse.

Study programme competencies
Code Study programme competences
A12 CE12 - Interpretar e representar correctamente o espazo tridimensional, coñecendo os obxectivos e o emprego dos sistemas de representación gráfica.
A14 CE14 - Avaliación cualitativa e cuantitativa de datos e resultados, así como a representación e interpretación matemáticas de resultados obtidos experimentalmente.
A17 CE17 - Modelizar situacións e resolver problemas con técnicas ou ferramentas físico-matemáticas.
B1 CT1 - Capacidad para gestionar los propios conocimientos y utilizar de forma eficiente técnicas de trabajo intelectual
B2 CT2 - Resolver problemas de forma efectiva.
B3 CT3 - Comunicarse de xeito efectivo nun ámbito de traballo.
B4 CT4 - Traballar de forma autónoma con iniciativa.
B5 CT5 - Traballar de forma colaboradora.
B6 CT6 - Comportarse con ética e responsabilidade social como cidadán e como profesional.
B7 CT7 - Capacidade para interpretar, seleccionar e valorar conceptos adquiridos noutras disciplinas do ámbito marítimo, mediante fundamentos físico-matemáticos.
B8 CT8 - Versatilidade.
B9 CT9 - Capacidade para a aprendizaxe de novos métodos e teorías, que lle doten dunha gran versatilidade para adaptarse a novas situacións.
B10 CT10 - Comunicar por escrito e oralmente os coñecementos procedentes da linguaxe científica.
B11 CT11 - Capacidade para resolver problemas con iniciativa, toma de decisións, creatividade, razoamento crítico e de comunicar e transmitir coñecementos habilidades e destrezas.
C1 C1 - Expresarse correctamente, tanto de forma oral coma escrita, nas linguas oficiais da comunidade autónoma.
C3 C3 - Utilizar as ferramentas básicas das tecnoloxías da información e as comunicacións (TIC) necesarias para o exercicio da súa profesión e para a aprendizaxe ao longo da súa vida.
C6 C6 - Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse.
C7 C7 - Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida.
C8 C8 - Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade.
C9 CB1 - Demostrar que posúen e comprenden coñecementos na área de estudo que parte da base da educación secundaria xeneral, e que inclúe coñecementos procedentes da vanguardia do seu campo de estudo
C10 CB2 - Aplicar os coñecementos no seu traballo ou vocación dunha forma profesional e poseer competencias demostrables por medio da elaboración e defensa de argumentos e resolución de problemas dentro da área dos seus estudos
C11 CB3 - Ter a capacidade de reunir e interpretar datos relevantes para emitir xuicios que inclúan unha reflexión sobre temas relevantes de índole social, científica ou ética
C12 CB4 - Poder transmitir información, ideas, problemas e solucións a un público tanto especializado como non especializado.
C13 CB5 - Ter desenvolvido aquelas habilidades de aprendizaxe necesarias para emprender estudos posteriores con un alto grao de autonomía.

Learning aims
Learning outcomes Study programme competences
A12
A14
A17
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B11
C1
C3
C6
C7
C8
C9
C10
C11
C12
C13

Contents
Topic Sub-topic
Lesson 1.- Bilinear forms. Quadratic forms.
 1.1.- Bilinear forms. Associated Matrix
1.2.- Symmetrical bilinear forms
1.3.- Quadratic forms
1.4.- Canonical Quadratic form. Reduction to the Canonical Form
1.5.- Classification of the Quadratic Forms
Lesson 2.- Loci in the Plane. Conic sections

 2.1.- Loci in the plane
2.2-. Circumference
2.3.- Elipse
2.4.- Hyperbola. Equilateral hyperbola.
2.5.- Parabola
2.6.- Conic sections.

Lesson 3.- General Equation of a Conic Section. Canonical Form 3.1.- General equation
3.2.- Invariants
3.3.- Classification
3.4.- Reduction to the Canonical Form
3.5.- Obtention of Relevant Elements: Centre, Axes, Asymptotes, Focus, Vertices
3.6.- Graphic representation

Lesson 4.- Loci in the space. Quadric surfaces

 4.1.- Loci in the Space
4.2.- Ruled surfaces. Surfaces of Revolution
4.3.- Spherical surface
4.4.- Ellipsoid
4.5.- Hyperboloids
4.6.- Paraboloids
4.7.- Cylindrical surfaces
4.8- Conical Surfaces

Lesson 5.- Functions of several real variables. Limits and Continuity. 10.1.- General definitions

 5.1.- General definitions
5.2.- Limits
5.3.- Continuity
Lesson 6.- Partial and Directional Derivatives

 6.1.- Partial Derivatives. Tangent Plane
6.2.- Directional Derivatives
6.3.- On Partial Derivatives, Directional Derivatives and Continuity
6.4.- Higher Order Partial derivatives.

Lesson 7.- Differentiation


 7.1.- General definitions
7.2.- Differentiability, Continuity and Partial Derivatives
7.3.- Chain Rules. Implicit Differentiation
7.4.- Higher order Differentiation

Lesson 8. Taylor's Theorem. Optimization

 8.1.- Taylor’s polinomyal and theorem
8.2.- Relative extrema
8.3.- Conditioned extrema. Lagrange Multipliers.
Lesson 9.- Multiple Integrals. Applications 9.1.- General definitions and Properties
9.2.- Iterated Integrals. Fubini's Theorem.
9.3.- Change of Variables
9.4.- Applications
Lesson 10.- Line Integral and Surface Integral 10.1.- Introduction
10.2.- Line Integral
10.3.- Green's Theorem
10.4.- Surface Integral
10.5.- Surface Integral in Curvilinear Coordinates
10.6.- Stoke's Theorem. Gauss-Ostrogradski's Theorem
Lesson 11.- Ordinary Differential Equations of First Order
 11.1.- General definitions
11.2.- Ordinary Differential Equations of First Order
11.3.- Main Types of ODE of First Order
Lesson 12.- Higher Order Ordinary Differential Equations 12.1.- Homogeneous and Nonhomogeneous Second Order ODE’s
12.2.- Second Order Linear ODE with constant coefficients
12.3.- Higher order Nonhomogeneous ODE of n-th Order
Lesson 13.- Systems of Ordinary Differential Equations 13.1.- Systems of Ordinary Differential Equations
13.2.- Systems of Linear Differential Equations with Constant Coefficients
Lesson 14.- Laplace Transform. Integraton by Series
 14.1.- Laplace Transform
14.2.- Applications of the Laplace Transform
14.3.- Integration of Ordinary Differential Equations by Series
The development and overcoming of these contents, together with those corresponding to other subjects that include the acquisition of specific competencies of the degree, guarantees the knowledge, comprehension and sufficiency of the competencies contained in Table AIII / 2, of the STCW Convention, related to the level of management of First Engineer Officer of the Merchant Navy, on ships without power limitation of the main propulsion machinery and Chief Engineer officer of the Merchant Navy up to a maximum of 3000 kW. Table A-III / 2 of the STCW Convention.
Specification of the minimum standard of competence for Chief Engineer Officers and First Engineer Officers on ships powered by main propulsion machinery of 3000 kW or more.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Collaborative learning A12 A14 A17 B2 B3 B5 B6 B8 B9 B10 B11 C1 C3 C6 C7 C8 C9 C10 C11 C12 C13 6 6 12
Diagramming A17 B1 B2 B3 B4 B7 B10 C1 C3 C6 2 4 6
Objective test A12 A14 A17 B1 B2 B3 B4 B6 B7 B8 B10 B11 C1 C3 C6 C8 4 0 4
Guest lecture / keynote speech A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B9 B10 B11 C1 C3 C6 C7 C8 27 27 54
Problem solving A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C3 C6 C7 C8 9 27 36
Supervised projects A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C6 C7 C8 4 20 24
Document analysis A12 A14 A17 B1 B4 B5 B7 B8 B9 B10 B11 C3 C6 C8 0 2 2
Online discussion A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C6 C7 C8 0 6 6
Directed discussion A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C6 C7 C8 2 0 2
 
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
Collaborative learning Resolver cuestións propostas en grupo e plantexar dudas.
Diagramming Resumir os conceptos máis importantes de cada tema.
Objective test Resolver de forma individual un test de coñecementos teóricos e prácticos.
Guest lecture / keynote speech Exposición dos temas.
Problem solving Resolución de exercicios tipo e proposta de outros a resolver por os estudantes.
Supervised projects Seguimento e corrección de traballos propostos.
Document analysis Seleccionar libros e páxinas web a utilizar
Online discussion Plantexar e resolver dudas en Moodle
Directed discussion Discusión na aula do plantexado previamente en Moodle.

Personalized attention
Methodologies
Collaborative learning
Problem solving
Supervised projects
Description
The students are encouraged to attend in small groups or individually to the professors' office to solve questions that may arise, thus obtaining a more specific guidance, acoording to their specific difficulties.

Assessment
Methodologies Competencies Description Qualification
Directed discussion A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C6 C7 C8 Participación nos debates na aula.
Se avaliarán as competencias A12, A14, A17, B1, B2, B3, B5, B6, B7, B8, B9, B10, B11, C1, C3, C5, C6, C7 y C8. 		5
Collaborative learning A12 A14 A17 B2 B3 B5 B6 B8 B9 B10 B11 C1 C3 C6 C7 C8 C9 C10 C11 C12 C13 Participación en traballos grupais.
Se avaliarán as competencias A12, A14, A17, B1, B2, B5, B6, B7, B8, B9, B10, B11, C1, C6, C7 y C8. 		5
Objective test A12 A14 A17 B1 B2 B3 B4 B6 B7 B8 B10 B11 C1 C3 C6 C8 Proba individual de asimilación de coñecementos
teórico-prácticos.
Se avaliarán as competencias A12, A14, A17, B1, B2, B5, B6, B7, B8, B9, B10, B11, C1, C6, C7 y C8. 		70
Problem solving A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C3 C6 C7 C8 Capacidade para resolver problemas.
Se avaliarán as competencias A12, A14, A17, B1, B2, B4, B5, B6, B8, B9, B10, B11, C1, C3, C6, C7 y C8. 		10
Supervised projects A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C6 C7 C8 Realización dos traballos propostos.
Se avaliarán as competencias A12, A14, A17, B1, B2, B4, B6, B7, B8, B9, B10, B11, C1, C5, C6, C7 y C8. 		10
 
Assessment comments

The course is divided into two parts: Part 1 (lessons 1-4) and part 2 (lessons 5-14). To pass it, it will be necessary to reach in each part a minimum of 3,5 points and afterwards obtain an average of, at least, 5 points following the formula (part 1+2*part 2)/3.

In the unlikely case of reaching  an arithmetic average of 5 but not having, at least, 3,5 points in each one of the parts, the result of the evaluation will be of fail and the final qualification will be calculated with a suitable geometric average.

The students that do not participate in the EHEA will be evaluated through a written test that will constitute 100% of the evaluation.  For those who participate in the EHEA, the written tests will constitute 70% of the final marks.  In order to add the qualification of the continuous assessment to the qualification of the written test, the latter must be at least 2,4 points (approximately 35% of 7) for each part, otherwise the final mark will only account for the written test.

Those students with recognition of part-time dedication and academic exemption of attendance, as established by the norm that regulates the regime of dedication to the study of undergraduate students in the UDC (Arts 2.3, 3.b, 4.3 e 7.5 ) (04/05/2017), and want to benefit from continuous assessment, must attend at least 50% of the course, exempting them from attending the theoretical classes, if they can not attend them. In case of not being able to attend the practical tests, they should attend tutorials at the proffesor office, where they will perform equivalent tests. 

Sources of information
Basic Granero, F. (). ALGEBRA LINEAL Y GEOMETRÍA. Mac Graw Hill
García García-López Pellicer (). ALGEBRA LINEAL Y GEOMETRÍA. Marfil
Fernández Viña, J.A. (). ANÁLISIS MATEMÁTICO II . Tecnos
Larson-Hostetler-Edwards (). CÁLCULO (2) . Mac Graw Hill
García, Alfonsa y otros (). CÁLCULO II . Librería ICAI
James Stewart (). CALCULO MULTIVARIABLE. Thomson
Martínez Sagarzazu (). ECUACIONES DIFERENCIALES. APLICACIONES Y EJERCICIOS. Universidad del País Vasco
Fernández Viña, J.A (). EJERCICIOS Y COMPLEMENTOS DE ANÁLISIS MATEMÁTICO II. Tecnos
Gutiérrez Gómez-García Castro (). GEOMETRÍA. Pirámide
D.G. Zill, W.S. Wright, J. Ibarra (). Matemáticas 3. Cálculo de Varias Variables. McGraw Hill
Villa, A. de la (). PROBLEMAS DE ÁLGEBRA LINEAL. Glagsa

Complementary


Recommendations
Subjects that it is recommended to have taken before
Mathematics I/631G02151

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus

Other comments


(*)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.