Study programme competencies |
Code
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Study programme competences / results
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A73 |
CE73 - Modelizar situacións e resolver problemas con técnicas ou ferramentas físico-matemáticas. |
A74 |
CE74 - Avaliar de forma cualitativa e cuantitativa os datos e resultados, así como a representación e interpretación matemáticas de resultados obtidos experimentalmente. |
A75 |
CE75 - Interpretar e representar correctamente o espazo tridimensional, coñecendo os obxectivos e o emprego dos sistemas de representación gráfica. |
B1 |
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 vangarda do seu campo de estudo |
B3 |
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 |
B4 |
CB4 - Poder transmitir información, ideas, problemas e solucións a un público tanto especializado como non especializado. |
B5 |
CB5 - Ter desenvolvido aquelas habilidades de aprendizaxe necesarias para emprender estudos posteriores con un alto grao de autonomía. |
B6 |
CG01 - Capacidade para xestionar os propios coñecementos e utilizar de forma eficiente técnicas de traballo intelectual. |
B7 |
CG02 - Resolver problemas de forma efectiva. |
B8 |
CG03 - Comunicarse de maneira efectiva nunha contorna de traballo. |
B9 |
CG04 - Traballar de forma autónoma con iniciativa. |
B10 |
CG05 - Traballar de forma colaborativa. |
B11 |
CG06 - Comportarse con ética e responsabilidade social como cidadán e como profesional. |
B12 |
CG07 - Capacidade para interpretar, seleccionar e valorar conceptos adquiridos noutras disciplinas do ámbito mariño, mediante fundamentos físico-matemáticos. |
B13 |
CG08 - Capacidade para a aprendizaxe de novos métodos e teorías, que lle doten dunha gran versatilidade para adaptarse a novas situacións. |
B14 |
CG09 - Comunicar por escrito e oralmente os coñecementos procedentes da linguaxe científica. |
B15 |
CG10 - Capacidade para resolver problemas con iniciativa, toma de decisións, creatividade, razoamento crítico e de comunicar e transmitir coñecementos habilidades e destrezas. |
B16 |
CG11 - Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse. |
B17 |
CG12 - Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida. |
B18 |
CG13 - Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade. |
C1 |
CT01 - Expresarse correctamente, tanto de forma oral como escrita, nas linguas oficiais da comunidade autónoma. |
C3 |
CT03 - 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. |
C7 |
CT07 - Desenvolver a capacidade de traballar en equipos interdisciplinares ou transdisciplinares, para ofrecer propostas que contribúan a un desenvolvemento sostible ambiental, económico, político e social. |
C8 |
CT08 - Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade. |
C9 |
CT09 - Ter a capacidade de xestionar tempos e recursos: desenvolver plans, priorizar actividades, identificar as críticas, establecer prazos e cumprilos. |
Learning aims |
Learning outcomes |
Study programme competences / results |
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A73 A74 A75
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B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18
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C1 C3 C7 C8 C9
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Contents |
Topic |
Sub-topic |
Lesson 1.- Bilinear forms. Quadratic forms.
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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
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Lesson 2.- Loci in the Plane. Conic sections
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2.1.- Loci in the plane
2.2-. Circumference
2.3.- Elipse
2.4.- Hyperbola. Equilateral hyperbola.
2.5.- Parabola
2.6.- Conic sections.
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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
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Lesson 4.- Loci in the space. Quadric surfaces
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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
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Lesson 5.- Functions of several real variables. Limits and Continuity. 10.1.- General definitions
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5.1.- General definitions
5.2.- Limits
5.3.- Continuity
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Lesson 6.- Partial and Directional Derivatives
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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.
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Lesson 7.- Differentiation
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7.1.- General definitions
7.2.- Differentiability, Continuity and Partial Derivatives
7.3.- Chain Rules. Implicit Differentiation
7.4.- Higher order Differentiation
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Lesson 8. Taylor's Theorem. Optimization
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8.1.- Taylor’s polinomyal and theorem
8.2.- Relative extrema
8.3.- Conditioned extrema. Lagrange Multipliers.
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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
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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
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Lesson 11.- Ordinary Differential Equations of First Order
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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
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Lesson 13.- Systems of Ordinary Differential Equations |
13.1.- Systems of Ordinary Differential Equations
13.2.- Systems of Linear Differential Equations with Constant Coefficients
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Lesson 14.- Laplace Transform. Integraton by Series
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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 / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A75 B3 B5 B6 B17 B18 C8 C9 |
28 |
28 |
56 |
Collaborative learning |
B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B13 B17 C1 C8 |
16 |
32 |
48 |
Problem solving |
A73 A74 A75 B3 B4 B5 B6 B7 B12 |
8 |
12 |
20 |
Supervised projects |
A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C3 C1 |
0 |
10 |
10 |
Seminar |
B1 B3 B5 B6 B7 B8 B9 B10 |
0 |
10 |
10 |
Document analysis |
B9 B10 B13 B16 C3 C7 C8 C9 |
0 |
3 |
3 |
Objective test |
B1 B8 B11 B14 B15 C1 C9 C8 |
2 |
0 |
2 |
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Personalized attention |
|
1 |
0 |
1 |
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(*)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. |
Collaborative learning |
Group work with presentation of the results when appropriate. |
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
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Problem solving |
Supervised projects |
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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.
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), in order to avoid face-to-face interaction in office. |
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Assessment |
Methodologies
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Competencies / Results |
Description
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Qualification
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Collaborative learning |
B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B13 B17 C1 C8 |
Participación en traballos grupais. |
5 |
Objective test |
B1 B8 B11 B14 B15 C1 C9 C8 |
Comprobación dos coñecementos e capacidade de resolución de problemas.
|
60 |
Problem solving |
A73 A74 A75 B3 B4 B5 B6 B7 B12 |
Resolver problemas. |
20 |
Supervised projects |
A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C3 C1 |
Realización dos traballos propostos. |
15 |
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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.
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Sources of information |
Basic
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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 |
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Complementary
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Recommendations |
Subjects that it is recommended to have taken before |
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Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
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