Identifying Data 2022/23
Subject (*) Mathematics II Code 631G01106
Study programme
Grao en Náutica e Transporte Marítimo
Descriptors Cycle Period Year Type Credits
Graduate 2nd four-month period
 First Basic training 6
Language
Spanish
Galician
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Arós Rodríguez, Angel Daniel
 E-mail
angel.aros@udc.es
Lecturers
Arós Rodríguez, Angel Daniel
Cao Rial, María Teresa
 E-mail
angel.aros@udc.es
teresa.cao@udc.es
Web http://www.nauticaymaquinas.es/
General description Nesta materia danse a coñecer conceptos fundamentais de Trigonometría Plana e Esférica, Lugares Xeométricos no Plano e o Espazo (en particular de Cónicas e Cuádricas), Derivación e Integración de funcións de varias variables e Estatística.
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
A2 Interpretar e representar correctamente o espazo tridimensional, coñecendo os obxectivos e o emprego de representación gráfica.
A8 Modelizar situacións e resolver problemas con técnicas ou ferramentas físico-matemáticas.
A9 Avaliación cualitativa e cuantitativa de datos e resultados, así como representación e interpretación matemática de resultados obtidos experimentalmente.
B1 Aprender a aprender.
B2 Resolver problemas de xeito efectivo.
B3 Aplicar un pensamento crítico, lóxico e creativo.
B4 Comunicarse de xeito efectivo nun ámbito de traballo.
B5 Traballar de forma autónoma con iniciativa.
B6 Traballar de forma colaboradora.
B7 Comportarse con ética e responsabilidade social como cidadán e como profesional.
B9 Capacidade para interpretar, seleccionar e valorar conceptos adquiridos noutras disciplinas do ámbito marítimo, mediante fundamentos físico-matemáticos.
B10 Versatilidade.
B11 Capacidade de adaptación a novas situacións.
B12 Uso das novas tecnoloxías TIC, e de Internet como medio de comunicación e como fonte de información.
B13 Comunicar por escrito e oralmente os coñecementos procedentes da linguaxe científica.
B14 Capacidade de análise e síntese.
B15 Capacidade para adquirir e aplicar coñecementos.
B16 Organizar, planificar e resolver problemas.
B17 Expresarse correctamente, tanto de forma oral coma escrita, nas linguas oficiais da comunidade autónoma
B19 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.
B22 Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse.
B23 Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida.
B24 Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade.
C9 Posuír e comprender coñecementos que aporten unha base ou oportunidade de ser originais no desenvolvemento e/ou aplicación de ideas, a miúdo nun contexto de investigación
C10 Que os estudantes saiban aplicar os coñecementos adquiridos e a súa capacidade de resolución de problemas en contornas novas ou pouco coñecidas dentro de contextos máis amplas (ou multidisciplinares) relacionados coa súa área de estudo

Learning aims
Learning outcomes Study programme competences
Escribir y transmitir conocimientos correctamente. B4
B13
B14
B17
Realizar eficazmente las tareas asignadas como parte del grupo. B3
B4
B6
B10
B16
Ser capaz de resolver y analizar los resultados de los problemas matemáticos que puedan plantearse en la ingeniería. A2
A8
A9
 B2
B5
B9
B15
 C9
Usar modelos matemáticos e identificar el caso en que deben aplicarse. A8
 B11
B22
B24
 C10
Conocer los conceptos fundamentales de Trigonometría Plana y Esférica, Lugares Geométricos en el Plano y el Espacio. Cónicas y Cuádricas, Derivación e Integración de funciones de varias variables y Estadística. A2
A8
A9
 B1
B2
B3
B9
B13
B14
B15
B16
B17
Mejorar habilidades en el aprendizaje y desarrollo de nuevos métodos y tecnologías necesarias para continuar su formación. B7
B12
B19
B23
Trabajar con material bibliográfico y recursos informáticos. B12
B15
B19
B22
B24
Elaborar una memoria/informe de modo riguroso y sistemático. B14
B15
B16
B17

Contents
Topic Sub-topic
Lesson 1.- Circular Functions. Formulas 1.1. Basic definitions and relationships
1.2. Graphical representations
1.3. Usual formulas
1.4. Inverse functions
1.5. Trigonometric equations
Lesson 2.- Planar Trigonometry. Solving Triangles. Applications. 2.1 Definitions
2.2. Laws of sines and cosines. other formulas
2.3. Solving Oblique Triangles
2.4. Complements and applications
Lesson 3.- Spherical triangles. General Properties. 3.1. Dihedral angles. The supplementary rectilinear
3.2. Trihedron. Polar trihedron
3.3. Spherical surface. Definitions
3.4. Spherical Triangle. Associated trihedron
3.5. Polar Spherical triangle. Properties
3.6. Accessories
Lesson 4.-Groups of Bessel’s formulas. Delambre and Neper analogies. 4.1. Bessel’s formulas
4.2. Briggs' formulas
4.3. Delambre-Gauss' analogies
4.4. Neper’s analogies
Tema 5.- Resolución de Triángulos Esféricos Oblicuángulos. 5.1. Análise de Casos
5.2. Complementos
Lesson 6.- Solving Oblique Spherical Triangles. 6.1. Definitions
6.2. General case: navigating a maximum circumference
6.3. Navegating a parallel
6.4. Navegating a plane
6.5. Estima (estimate position)
Lesson 5.- Solving Right-angled Spherical Triangles. 5.1. Definitions
5.2. Particular formulas. Napier’s nifty Rules
5.3. Particular propierties of the right triangles.
5.4. Solving right triangles.
5.5. Decomposition into right triangles. Perpendicular method.
Lesson 7.- Loci in the Plane. Conic sections. 7.1. Locus in the plane
7.2. Conic sections
7.2.1. Circle
7.2.2. Elipse
7.2.3. Hyperbola
7.2.4. Parabola
Lesson 9.-Loci in the space. Quadric surfaces. 9.1. Loci in the space
9.1.1. Quadric surfaces of revolution
9.1.3. Ruled surfaces
9.2. Particular estudy of Quadric surfaces
9.2.1. Sphere
9.2.2. Ellipsoid
9.2.3. Hyperboloids
9.2.4. Paraboloids
9.2.5. Degenerate quadric surfaces
9.3. General equation of Quadric surfaces
9.3.1. General equation
9.3.2. Invariantes métricos
9.3.3. Clasification
9.4.4. Reduction to Canonical form
Lesson 10.- Functions of several real variables. Limits and Continuity. 10.1.- General definitions
10.2.- Limits
10.3.- Continuity
Lesson 11. Partial and Directional Derivatives. Taylor’s formula. Extrema. 11.1.- Partial derivatives. Tangent plane
11.2.- Directional Derivatives.
11.3.- Higher order Derivatives
11.4.- Taylor’s polinomyal and theorem
11.5.- Relative extrema and conditioned extrema.
Lesson 12.- Integrals in two and three variables. Calculus and applications 12.1.- General definitions
12.2.- Properties
12.3.- Iterated Integrals. Fubini’s Theorem.
12.4.- Change of Variables
12.5.- Applications
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 AII / 2, of the STCW Convention, related to the level of management of chief mates of the Merchant Navy, on ships without gross tonnage limitation and Master up to a maximum of 500 GT. Table A-II / 2 of the STCW Convention.

Mandatory minimum requirements for certification of masters and chief mates on chief on ships of 500 gross tonnage or more.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A2 A8 B1 B2 B3 B4 B15 B22 C9 C10 30 30 60
Problem solving A2 A8 A9 B5 B6 B10 B11 B12 B13 B15 B16 B17 B19 C10 24 36 60
Supervised projects A2 A8 A9 B1 B2 B3 B4 B5 B6 B9 B12 B13 B14 B15 B16 B17 B19 B22 B23 B24 C10 0 10 10
Seminar A2 A8 A9 B5 B6 B10 B11 B12 B13 B15 B16 B17 B19 C10 0 10 10
Document analysis B1 B2 B4 B5 B6 B7 B10 B11 B12 B14 B15 B16 B17 B19 0 3 3
Objective test A2 A8 A9 B2 B4 B5 B11 B12 B13 B14 B16 B17 B19 B22 C10 2 0 2
 
Personalized attention 5 0 5
 
(*)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 Exposition in the classroom of the fundamental concepts.
Problem solving In each topic, exercises will be proposed to solve.
Supervised projects Proposed individual and group projects.
Seminar Individual and / or very small group tutorships.
Document analysis Select books and web pages to use
Objective test Knowledge assessment.

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

Due to the health situation caused by COVID-19, and following the recommendations of the Center, the attention to students will preferably be held through computer hardware and the Internet (email and meetings by MS Teams).

Assessment
Methodologies Competencies Description Qualification
Objective test A2 A8 A9 B2 B4 B5 B11 B12 B13 B14 B16 B17 B19 B22 C10 Proba individual de asimilación de coñecementos.
 60
Guest lecture / keynote speech A2 A8 B1 B2 B3 B4 B15 B22 C9 C10 Resolución de cuestións teóricas ou prácticas breves relacionadas cos contidos da sesión maxistral 10
Supervised projects A2 A8 A9 B1 B2 B3 B4 B5 B6 B9 B12 B13 B14 B15 B16 B17 B19 B22 B23 B24 C10 Realización dos traballos propostos.
 15
Problem solving A2 A8 A9 B5 B6 B10 B11 B12 B13 B15 B16 B17 B19 C10 Capacidade para resolver problemas.
 15
 
Assessment comments

The students participants in the EHEA should attend a minimum of 80% of the lessons, being the continuous assessment of 40% of the final score. The other 60% of the score will be obtained from the partial tests that will take place throughout the term.

The students who have followed the continuous assessment but have not reached the 50% of the score through the partial tests will have a chance to reach it through a final test. This final test will include all topics of the term (the partial tests do not exclude topics). A student who does not do at least one of hte partial exams or a final exam will be qualified as Not Presented.

The students who decide to not take part in the EHEA will be evaluated  with an objective test that includes an individual test of assimilation of practical-theoretical knowledge and problem solving.

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 stay on the path of the EHEA and benefit from continuous assessment, must INDICATE SUCH CONDITION AT THE BEGINNING OF THE COURSE and attend at least 50% of the interactive lectures. In case of not being able to attend these sessions, they should attend tutorials at the proffesor office or by TEAMS, where they will perform equivalent tests. 

Fraudulent conduct in tests or activities, once verified, will cause a final mark of 0, invalidating any mark obtained in the in previous activities, as established in the current academic regulations at UDC.

Sources of information
Basic Larson-Hostetler-Edwards (). CÁLCULO (2) . Mac Graw Hill
D.G. Zill, W.S. Wright (). Cálculo de Varias Variables. McGraw Hill
Elizabeth Vargas, Luis A. Núñez (2020). Geometría III: geometría analítica plana y del espacio. UAPA
M.T. Cao Rial, Á. D. Rodríguez Arós (2020). Problemas de Trrigonometría Esférica. Aplicaciones a la navegación. Universidade da Coruña
A. R. Arós, F. Blanco, M.J. Muiños (2012). TRIGONOMETRÍA PLANA Y ESFÉRICA CON APLICACIONES A LA NAVEGACIÓN. Paraninfo

Complementary James Stewart (). CALCULO MULTIVARIABLE. Thomson Editores
Vila Mitjá, A. (). ELEMENTOS DE TRIGONOMETRÍA ESFÉRICA. U.P.C.
Gutiérrez Gómez-García Castro (). GEOMETRÍA. Pirámide
Villa, A. de la (). PROBLEMAS DE ÁLGEBRA LINEAL. Glagsa
Swokowski-Kole (). TRIGONOMETRÍA. Thomson
Ayres, F. (). TRIGONOMETRÍA PLANA Y ESFÉRICA. Mac Graw Hill


Recommendations
Subjects that it is recommended to have taken before
Mathematics I/631G01101

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus
Navigation I/631G01202
Ship Manoeuvering I/631G01207
Ship's Theory I/631G01208

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.