Study programme competencies |
Code
|
Study programme competences / results
|
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 |
Escribir e transmitir coñecementos correctamente. |
|
B3 B4 B11
|
C1
|
Realizar eficazmente as tarefas asignadas como parte dun grupo. |
|
B4 B8 B10
|
C1 C7
|
Ser capaz de resolver e analizar os resultados dos problemas matemáticos que poidan plantexarse na enxeñaría. |
A73 A74 A75
|
B3 B6 B7 B9 B12 B13 B15
|
C3 C9
|
Usar modelos matemáticos e identificar o caso no que deben aplicarse. |
A73 A74 A75
|
B1 B3 B6 B7 B13 B15
|
|
Coñecer os conceptos fundamentais e aplicacións da Álgebra Lineal, Xeometría do Plano e do Espacio Afín e Euclídeo, Análisis de Funcións Reais dunha Variable Real e Variable Complexa. |
A73 A74 A75
|
B1 B3 B5 B6 B7 B9 B13 B15
|
|
Manexar con soltura as ferramentas básicas da Álxebra e o Cálculo. |
A73 A74 A75
|
B1 B7 B9 B11
|
C3 C7 C8 C9
|
Mellorar habilidades na aprendizaxe e desenvolvemento de novos métodos e tecnoloxías necesarias para continuar a súa formación. |
|
B3 B5 B11 B13 B16 B17 B18
|
C8
|
Traballar con material bibliográfico e recursos informáticos. |
|
|
C3 C8
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Elaborar unha memoria/informe de modo científico, estruturado, rigoroso e conciso. |
|
B3 B4 B7 B8 B9 B14
|
C1 C8 C9
|
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.
|
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.
|
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.
|
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.
|
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.
|
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.
|
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.
|
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.
|
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.
|
Lesson 15.- Indefinite integration of Functions of a Real Variable
|
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.
|
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. |
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 |
Problem solving |
A73 A74 A75 B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B17 C1 C7 C8 |
24 |
36 |
60 |
Supervised projects |
A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C1 C3 C7 C8 |
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 |
Introductory activities |
B1 B4 B5 |
2 |
2 |
4 |
Objective test |
B1 B8 B11 B14 B15 C1 C7 C8 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 |
Methodologies
|
Seminar |
Supervised projects |
|
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), in order to avoid face-to-face interaction in office. |
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Supervised projects |
A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C1 C3 C7 C8 |
Traballos propostos.
|
15 |
Objective test |
B1 B8 B11 B14 B15 C1 C7 C8 C9 |
Comprobación dos coñecementos e capacidade de resolución de problemas.
|
60 |
Guest lecture / keynote speech |
A75 B3 B5 B6 B17 B18 C8 C9 |
Preguntas sobre cuestións teóricas |
10 |
Problem solving |
A73 A74 A75 B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B17 C1 C7 C8 |
Resolver problemas. |
15 |
|
Assessment comments |
The students participating in the EHEA should take a minimum of 75% of the continuous assessment (c.a.) tests done in the classroom. These c.a. test might be posed either on keynote lectures or problem solving sessions, and they represent the 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 the sessions where c.a. tests where taken, they should attend tutorials at the proffesor office or by TEAMS, where they will perform equivalent tests. Both opportunities: Fraud in tests or evaluation activities, once verified, will directly imply failing the subject in which it has been committed: the student will be receive a final mark equal to 0, whether the commission of the fraud happens on the first opportunity or on the second. To do this, the qualification of the first opportunity will be modified, if necessary.
|
Sources of information |
Basic
|
R.E. Larson, R.P. Hostetler, B.H. Edwards (1999). Cálculo. McGraw Hill
D.G. Zill, W.S. Wright, J. Ibarra (). Matemáticas 1. Cálculo Diferencial. McGraw Hill
D.G. Zill, W.S. Wright, J. Ibarra (). Matemáticas 2. Cálculo Integral. McGraw Hill
S. Grossman, J. Ibarra (). Matemáticas 4. Álgebra Lineal. McGraw Hill
Á.M. Ramos del Olmo, J.M. Rey Cabezas (2017). Matemáticas básicas para el acceso a la universidad. Pirámide |
|
Complementary
|
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
Granero, F. (). EJERCICIOS Y PROBLEMAS DE CÁLCULO (I y II). Tébar Flores
Villa, A. de la (). PROBLEMAS DE ALGEBRA LINEAL. GLAGSA |
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Recommendations |
Subjects that it is recommended to have taken before |
|
Subjects that are recommended to be taken simultaneously |
|
Subjects that continue the syllabus |
Numerical and Statistical Methods/631G03011 | Mathematics II/631G03006 |
|
Other comments |
<p>Attend the optional introductory course the first week.</p> |
|