Study programme competencies |
Code
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Study programme competences / results
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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 / results |
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A12 A14 A17
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B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
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C1 C3 C6 C7 C8 C9 C10 C11 C12 C13
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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 |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
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 |
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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 |
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. |
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Assessment |
Methodologies
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Competencies / Results |
Description
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Qualification
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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 |
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Assessment comments |
The students that do not participate in the EEES will be evaluated through an Objective Proof that will constitute 100% of the evaluation. The course is divided in 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 to reach 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 criteria of evaluation contemplated in the framewor A-III/1 and A-III/2 of the Code STCW and his amendments related with this matter have been taken into account for the design of this qualification methodology.
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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
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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