Study programme competencies |
Code
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Study programme competences
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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. |
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 |
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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 C5 C6 C7 C8 C9 C10 C11 C12 C13
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Contents |
Topic |
Sub-topic |
Lesson 1.- Vector Space |
1.1.- Vector space. Definition. Examples and Properties
1.2.- Vector subspace.
1.3.- System of Generators of a Subspace
1.4.- Linear Independence
1.5.- Basis of a Vector Space. Finite Dimensional Spaces.
1.6.- Change of Basis in a Vector Space
1.7.- Union and Intersection of Subspaces
1.8.- Sum of Subspaces. Direct sum. Supplementary Subspaces.
1.9.- Product of Vectorial Spaces |
Lesson 2.- Linear Functions. Matrices. |
2.1.- Linear Function: Definition, Examples, Properties and Types of Linear Functions.
2.2.- Kernel and Image of a Linear Function.
2.3.- Existence and obtention of an Associated Matrix to a Linear Function.
2.4.- Addition of Linear Functions. Product by a Scalar. Associated Matrices.
2.5.- Vector Spaces of Matrices
2.6.- Composition of Linear Functions. Associated Matrix.
2.7.- Product of Matrices. Ring of Square Matrices
2.8.- Some Particular Types of Matrices
2.9.- Transpose Matrix. Symmetric, Antisymmetric and Orthogonal Matrices.
2.10.- Matrices of Complex Elements. |
Lesson 3.- Determinants.
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3.0.- Permutations. Class of a Permutation.
3.1.- Determinant of a Square Matrix. Sarrus Rule.
3.2.- Properties of Determinants.
3.3.- Methods for Calculation of Determinants. Cofactor Matrix.
3.4.- Product of Determinants.
3.5.- Some Particular Examples of Determinants.
3.6.- Reverse Matrix.
3.7.- Rank of a Matrix.
3.8.- Rank of a System of Vectors
3.9.- Expression of the Change of Base of a Vectorial Space in shape Matrix |
Lesson 4.- Systems of Linear Equations.
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4.1.- Definitions. Classification. Matrix notation.
4.2.- Equivalent systems.
4.3.- System of Cramer. Rule of Cramer
4.4.- General System of Linear Equations. Theorem of Rouché-Frobenius
4.5.- Homogeneous Systems.
4.6.- Methods of Resolution by Reduction. Gauss' Method. |
Lesson 5.- Matrix Diagonalization.
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5.1.- Eigenvectors and Eigenvalues. Properties.
5.2.- Characteristic polynomial. Properties.
5.3.- Diagonalizable Matrices. Diagonalization.
5.4.- Diagonalization Of Symmetric Matrices. |
Lesson 6.- Affine Space E3. Problems of Incidence and Parallelism.
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6.1.- Affine Space Associated to a Vector Space. System of Reference. Coordinates.
6.2.- Equations of Straight Lines.
6.3.- Relative positions of Straight Lines.
6.4.- Equations of a Plane.
6.5.- Relative positions of Planes. Bundles of Planes.
6.6.- Relative positions of Straight Lines and Planes. |
Lesson 7.- Euclidean Vector Spaces. Scalar product, Vector product. Mixed Product. |
7.1.- Scalar product
7.2.- Determination of a Scalar Product. Gram Matrix.
7.3.- Euclidean Vector Space. Definition.
7.4.- Norm of a Vector. Relevant Equalities and Inequalities.
7.5.- Angle of two Vectors. Orthogonality.
7.6.- Orthonormal Basis. Expression of the Scalar Product in an Orthonormal Basis.
7.7.- Euclidean Space E3.
7.8.- Orientation in E3.
7.9.- Vector product in R3 . Properties. Analytical expression.
7.10.- Mixed product. Analytical expression. Geometrical interpretation.
7.11.- Combined Products. |
Lesson 8.- Metric Problems in Euclidean Spaces.
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8.1.- Normal equation of a Plane.
8.2.- Angles between Linear Manifolds in R3: Angle of Two Planes, Angle of Two Straight Lines, Angle of Straight Line and Plane.
8.3.- Distance between Linear Manifolds in R3: Distance of a Point to a Plane, Distance of a Point to a Straight Line. Distance between two Planes, Distance between Straight Line and Plane. Distance between two Straight Lines. Common Perpendicular to two Straight Lines.
8.4.- Cylindrical coordinates and Spherical coordinates in R3. |
Lesson 9.-Real valued functions of a Real Variable. Continuity.
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9.1.- Basic definitions.
9.2.- Functional limits.
9.3.- Continuity. Types of Discontinuity.
9.4.- Properties and Theorems on Continuous Functions. |
Lesson 10.- Differentiability and Applications of the Derivatives.
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10.1.- Derivative and Differential of a Function in a Point. Geometrical meaning.
10.2.- Properties and Calculation of Derivatives.
10.3.- Derivative function. Successive derivatives.
10.4.- Applications of the Derivatives to the Local Study of a Function: Growth and Decreasing. Maxima and Minima. Concavity and Convexity. Inflection points.
10.5.- Theorems of Rolle and Mean Value Theorem.
10.6.- Rules of L´Hôpital |
Lesson 11.- Theorem of Taylor. Applications.
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11.1.- Expression of a Polynomial by means of his Derivatives in a Point.
11.2.- Polynomial and Theorem of Taylor. Formulae of Taylor and Mac Laurin.
11.3.- Expression of Lagrange for the Residual. Bounds for the residual.
11.4.- Applications to the Local Study of a Function: Monotonicity. Extremal values. Concavity and Convexity. Inflection points.
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Lesson 12.- Graphic representation of Real Valued Functions. |
12.1.- Domain and Continuity
12.2.- Symmetries
12.3.- Periodicity.
12.4.- Intersection with the coordinates axis.
12.5.- Use of successive derivatives and applications: Monotonicity. Extremal values. Concavity and Convexity. Inflection points.
12.6.- Asymptotes and Parabolic Branches |
Lesson 13.- Sequences and Series.
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13.1.- General definitions. Types of Sequences.
13.2.- Practical calculation of Limits
13.3.- General definitions. Main Types of Numerical Series.
13.4.- Properties of the Numerical Series. Criteria of Convergence for Series of Positive Terms.
13.5.- Series of Positive and Negative Terms. Alternated Series. |
Lesson 14.- Functional Sequences and Series. Series of powers.
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14.1.- General definitions.
14.2.- Series of Powers. Convergence.
14.3.- Series expansions.
14.4.- Series of Taylor and Mac Laurin.
14.5.- Binomial Series.
14.6.- Method of the Undetermined Coefficients. |
Lesson 15.- Indefinite integration of Functions of a Real Variable
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15.1.- General definitions. Table of Primitives.
15.2.- Immediate integration
15.3.- Integration by Parts
15.4.- Integration of Rational Functions
15.5.- Integration by Replacement or Change of Variable |
Lesson 16.- Definite Integration. Applications.
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16.1.- General definitions
16.2.- Properties
16.3.- Mean Value Theorem. Barrow's Rule.
16.4.- Evaluation of Definite Integrals.
16.5.- Improper Integral.
16.6.- Applications of the Definite Integral |
Lesson 17.- Complex Numbers |
17.1.- General definitions
17.2.- Fundamental operations
17.3.- Powers and Roots
17.4.- Exponential form of a Complex
17.5.- Logarithms And Complex Powers. |
Planning |
Methodologies / tests |
Competencies |
Ordinary class hours |
Student’s personal work hours |
Total hours |
Problem solving |
A12 A14 A17 B1 B2 B3 B4 B5 B7 B8 B9 B10 B11 C3 C6 C7 C8 C9 C10 C11 C12 C13 |
6 |
24 |
30 |
Guest lecture / keynote speech |
A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B9 C1 C3 C5 C7 C8 |
24 |
24 |
48 |
Objective test |
A12 A14 A17 B1 B2 B3 B4 B6 B7 B8 B10 B11 C1 C3 C5 C6 C8 |
4 |
0 |
4 |
Document analysis |
A12 A17 B1 B3 B4 B5 B7 B8 B9 B11 C3 |
0 |
2 |
2 |
Collaborative learning |
A12 A14 A17 B1 B2 B3 B5 B6 B7 B8 B9 B10 B11 C1 C3 C5 C6 C7 C8 |
9 |
9 |
18 |
Supervised projects |
A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C5 C6 C7 C8 |
4 |
20 |
24 |
Online discussion |
A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C5 C6 C7 C8 |
0 |
6 |
6 |
Directed discussion |
A12 A14 A17 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C5 C6 C7 C8 |
2 |
0 |
2 |
Diagramming |
A14 A17 B1 B2 B4 B5 B7 B8 B9 B10 C9 C11 C12 |
2 |
4 |
6 |
Introductory activities |
A12 A14 A17 B1 B4 B6 B7 B9 B10 C1 C3 C5 C6 C7 |
3 |
3 |
6 |
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Personalized attention |
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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 |
Problem solving |
En cada tema, vanse propoñer exercicios para resolver. |
Guest lecture / keynote speech |
Exposición na aula dos conceptos fundamentais. |
Objective test |
Proba de coñecementos. |
Document analysis |
Seleccionar libros e páxinas web a utilizar |
Collaborative learning |
Traballo en grupo con exposición dos resultados no seu caso |
Supervised projects |
Traballos propostos individuais e grupais |
Online discussion |
Plantexar e resolver dudas en Moodle |
Directed discussion |
Discusión na aula do plantexado previamente en Moodle ou en clase. |
Diagramming |
Facer esquemas |
Introductory activities |
Tema 0: Conceptos básicos que se deben recordar |
Personalized attention |
Methodologies
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Supervised projects |
Collaborative learning |
Guest lecture / keynote speech |
Problem solving |
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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. |
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Assessment |
Methodologies
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Competencies |
Description
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Qualification
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Directed discussion |
A12 A14 A17 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C5 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 |
Supervised projects |
A12 A14 A17 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C5 C6 C7 C8 |
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 |
Collaborative learning |
A12 A14 A17 B1 B2 B3 B5 B6 B7 B8 B9 B10 B11 C1 C3 C5 C6 C7 C8 |
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 C5 C6 C8 |
Comprobación dos coñecementos e capacidade de resolución de problemas.
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 B7 B8 B9 B10 B11 C3 C6 C7 C8 C9 C10 C11 C12 C13 |
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 |
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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 1-8) and part 2 (lessons 9-17). 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. 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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García Gómez - Gutiérrez Castro (). ALGEBRA LINEAL. Pirámide
Granero, F (). ALGEBRA Y GEOMETRÍA ANALÍTICA . Mac Graw-Hill
Fernández Viña, J.A (). ANÁLISIS MATEMÁTICO I . Tecnos
Granero, F. (). CÁLCULO . Mac Graw-Hill
García , A.y otros. (). CÁLCULO I (Teoría y Problemas) . Librería I.C.A.I
Fernández Viña, J.A (). EJERCICIOS Y COMPLEMENTOS DE ANÁLISIS MATEMÁTICO I. Tecnos
Granero, F. (). EJERCICIOS Y PROBLEMAS DE CÁLCULO (I y II) . Tébar Flores
García Gómez - Gutiérrez Castro. (). GEOMETRÍA . Pirámide
Villa, A. de la (). PROBLEMAS DE ALGEBRA 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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