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). Students not passing after taking the partial tests, and not taking the final tests will be qualified as NOT ATTENDING.

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.

The fraudulent performance of the tests or evaluation activities, once verified, will directly imply the failure grade, numerical qualification of 0, in the corresponding call, invalidating any grade obtained in the tests or evaluation activities, as established in the academic regulations at the UDC.

Learning outcomes	Study programme competences
Escribir e transmitir coñecementos correctamente.	A12 A14 A17	B3 B4 B10	C1 C10
Realizar eficazmente as tarefas asignadas como parte do grupo.		B3 B5
Ser capaz de resolver e analizar os resultados dos problemas matemáticos que poidan plantexarse na enxeñaría.	A14 A17	B2 B7 B11	C1 C9 C11
Usar modelos matemáticos e identificar o caso no que deben aplicarse.	A17	B1 B2 B7 B9
Coñecer os conceptos fundamentais e aplicacións de Álxebra Lineal, Xeometría do Plano e do Espazo Afín e Euclídeo, Análise de Funcións Reais dunha Variable Real e Variable Complexa.	A12 A14 A17	B1 B2 B7 B9 B11	C9 C11 C12
Manexar con soltura as ferramentas básicas de Álxebra e Cálculo.	A12 A14 A17	B1 B2 B7 B9 B11	C1 C10 C11 C12
Mellorar habilidades na aprendizaxe e desenvolvemento de novos métodos e tecnoloxías necesarias para continuar a súa formación.		B6 B8	C3 C5 C6 C7 C8 C13
Traballar con material bibliográfico e recursos informáticos.			C3 C6 C8 C11 C13
Elaborar unha memoria/informe de modo rigoroso e sistemático.	A14	B2 B3 B4 B7 B10	C1

Topic	Sub-topic
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 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 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.

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	B1 B3 B4 B7 C1 C7 C11	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	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.

Methodologies	Competencies	Description	Qualification
Guest lecture / keynote speech	A12 A14 A17 B1 B2 B3 B6 B7 B9 C6 C8	Preguntas sobre cuestións teóricas	10
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	Traballos propostos.	15
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). Students not passing after taking the partial tests, and not taking the final tests will be qualified as NOT ATTENDING. 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. The fraudulent performance of the tests or evaluation activities, once verified, will directly imply the failure grade, numerical qualification of 0, in the corresponding call, invalidating any grade obtained in the tests or evaluation activities, as established in the academic regulations at the UDC.

Basic	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. (). Álgebra 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 Álgebra Lineal. GLACSA

Other comments
&lt;p&gt;Attend the optional introductory course the first week.&lt;/p&gt;