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.

Fraudulent conduct in tests or activities, once verified, will cause a final mark of 0, invalidating any mark obtained in the in previous activities, as established in the current academic regulations at UDC.

Learning outcomes	Study programme competences
Escribir e transmitir coñecementos correctamente.		B3 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 de Álxebra Lineal, Xeometría do Plano e do Espacio Afín e Euclídeo, Análise de Funcións Reais dunha Variable Real e Variable Complexa.	A73 A74 A75	B1 B3 B5 B6 B7 B9 B13 B15
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
Elaborar unha memoria/informe de modo científico, estruturado, rigoroso e conciso.		B3 B4 B7 B8 B9 B14	C1 C8 C9

Topic	Sub-topic
Lesson 2.- Loci in the Plane. Conic sections	2.1.- Loci in the plane 2.2-. Circumference 2.3.- Elipse 2.4.- Hyperbola. Equilateral hyperbola. 2.5.- Parabola 2.6.- Conic sections.
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
Lesson 4.- Loci in the space. Quadric surfaces	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
Lesson 5.- Functions of several real variables. Limits and Continuity. 10.1.- General definitions	5.1.- General definitions 5.2.- Limits 5.3.- Continuity
Lesson 6.- Partial and Directional Derivatives	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.
Lesson 7.- Differentiation	7.1.- General definitions 7.2.- Differentiability, Continuity and Partial Derivatives 7.3.- Chain Rules. Implicit Differentiation 7.4.- Higher order Differentiation
Lesson 8. Taylor's Theorem. Optimization	8.1.- Taylor’s polinomyal and theorem 8.2.- Relative extrema 8.3.- Conditioned extrema. Lagrange Multipliers.
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
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
Lesson 11.- Ordinary Differential Equations of First Order	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
Lesson 13.- Systems of Ordinary Differential Equations	13.1.- Systems of Ordinary Differential Equations 13.2.- Systems of Linear Differential Equations with Constant Coefficients
Lesson 14.- Laplace Transform. Integraton by Series	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.

Methodologies / tests	Competencies	Ordinary class hours	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 C8	24	36	60
Supervised projects	A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C1 C3	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 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	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 asignatura
Objective test	Knowledge assessment.

Methodologies	Competencies	Description	Qualification
Objective test	B1 B8 B11 B14 B15 C1 C8 C9	Comprobación dos coñecementos e capacidade de resolución de problemas.	60
Guest lecture / keynote speech	A75 B3 B5 B6 B17 B18 C8 C9	Coñecementos teóricos	10
Problem solving	A73 A74 A75 B1 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B17 C1 C8	Resolver problemas.	15
Supervised projects	A73 B1 B3 B4 B6 B8 B9 B10 B14 B15 B16 C1 C3	Realización dos traballos propostos.	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) 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. Fraudulent conduct in tests or activities, once verified, will cause a final mark of 0, invalidating any mark obtained in the in previous activities, as established in the current academic regulations at UDC.

Basic	Larson-Hostetler-Edwards (). CÁLCULO (2) . Mac Graw Hill James Stewart (). CALCULO MULTIVARIABLE. Thomson Martínez Sagarzazu (). ECUACIONES DIFERENCIALES. APLICACIONES Y EJERCICIOS. Universidad del País Vasco Elizabeth Vargas, Luis A. Núñez (2020). Geometría III: geometría analítica plana y del espacio. UAPA 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

Complementary	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 García, Alfonsa y otros (). CÁLCULO II. Librería ICAI Fernández Viña, J.A. (). EJERCICIOS Y COMPLEMENTOS DE ANÁLISIS MATEMÁTICO II. Tecnos Gutiérrez Gómez-García Castro (). GEOMETRÍA. Pirámide

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