| 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. |
| C5 | C5 - Entender a importancia da cultura emprendedora e coñecer os medios ao alcance das persoas emprendedoras. |
| 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 | ||
| Escribir e transmitir coñecementos correctamente. | A12 A14 A17 |
B2 B7 B9 B10 |
C1 |
| Realizar eficazmente as tarefas asignadas como parte dun grupo. | B1 B3 B4 B5 B8 B11 |
C3 C6 C9 C10 |
|
| Será capaz de resolver e analizar os resultados dos problemas matemáticos que poidan plantexarse na enxeñaría. | B6 |
C7 C8 C11 C12 C13 |
|
| Usar os modelos matemáticos e identificar o caso no que deben aplicarse. | A17 |
B1 B2 B7 B9 |
|
| Coñecer os conceptos fundamentais de Xeometría, Análise de Funcións Reais de Varias Variables Reais e Ecuacións Diferenciais. | A12 A14 A17 |
B1 B2 B7 B9 B11 |
C9 C11 C12 |
| Mellorar habilidades na aprendizaxe e desenvolvemento de novos métodos e tecnoloxías necesarias para continuar a súa formación. | A12 A14 A17 |
B6 B8 |
C3 C5 C6 C7 C8 C13 |
| Traballar con material bibliográfico e recursos informáticos. | C3 C6 C13 |
||
| Elaborar unha memoria/informe de modo rigoroso e sistemático. | A14 |
B2 B3 B4 B7 B10 |
C1 |
| Contents |
| Topic | Sub-topic |
| 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 |
| Guest lecture / keynote speech | A12 A14 A17 B1 B2 B3 B6 B7 B9 C6 C8 | 28 | 28 | 56 |
| Problem solving | A12 A17 B2 B4 B6 B7 B8 B9 B10 B11 C1 C3 C9 C10 C11 C12 C13 | 24 | 36 | 60 |
| Supervised projects | A12 A17 B2 B3 B4 B7 B9 B10 C1 C9 C10 C12 | 0 | 10 | 10 |
| Seminar | A12 A14 A17 B2 C1 C3 C5 C6 C7 C8 C9 C10 C11 C12 C13 | 0 | 10 | 10 |
| Document analysis | A12 A17 B1 B3 B4 B5 B7 B8 B9 B11 C3 | 0 | 3 | 3 |
| Introductory activities | A12 B3 B4 B6 B7 B8 B9 B10 C1 | 2 | 2 | 4 |
| Objective test | A12 A14 A17 B1 B2 B3 B4 B6 B7 B10 B11 C1 C9 | 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 |
| Introductory activities | Introdución á materia |
| Objective test | Knowledge assessment. |
| Personalized attention |
|
|
| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Objective test | A12 A14 A17 B1 B2 B3 B4 B6 B7 B10 B11 C1 C9 | Comprobación dos coñecementos e capacidade de resolución de problemas. |
60 |
| Supervised projects | A12 A17 B2 B3 B4 B7 B9 B10 C1 C9 C10 C12 | Realización dos traballos propostos. | 15 |
| Guest lecture / keynote speech | A12 A14 A17 B1 B2 B3 B6 B7 B9 C6 C8 | Coñecementos teóricos | 10 |
| Problem solving | A12 A17 B2 B4 B6 B7 B8 B9 B10 B11 C1 C3 C9 C10 C11 C12 C13 | 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) 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
James Stewart (). CALCULO MULTIVARIABLE. Thomson
Martínez Sagarzazu (). ECUACIONES DIFERENCIALES. APLICACIONES Y EJERCICIOS. Universidad del País Vasco
Elizabeth Vargas, Luis A. Núñez (2020). Geometría III: geometría analítica plana y del espacio. UAPA
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 |
Granero, F. (). ÁLGEBRA LINEAL Y GEOMETRÍA. Mac Graw Hill
García García-López Pellicer (). ÁLGEBRA LINEAL Y GEOMETRÍA. Marfil
Fernández Viña, J. A. (). ANÁLISIS MATEMÁTICO II. Tecnos
García, Alfonsa y otros (). CÁLCULO ii. Librería ICAI
Fernández Viña, J. A. (). EJERCICIOS Y COMPLEMENTOS DE ANÁLISIS MATEMÁTICO II. Tecnos
Gutiérrez Gómez-García Castro (). GEOMETRÍA. Pirámide |
|
|
| Recommendations | |
| Subjects that it is recommended to have taken before | |
|
| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus |
| Other comments | |