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). A student who does not do at least one of hte partial exams or a final exam will be qualified as Not Presented.

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.

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.

Learning outcomes	Study programme competences
RA1C-Write, explain and transmit the theoretical knowledge acquired both orally and in writing using scientific-technical language.	A54
RA2C-Identify and relate acquired knowledge to other disciplines	A55
RA4C-Collecting and interpreting relevant data	A57
RA7H-Applying critical, logical and creative thinking		B30
RA9H-Effectively solve practical problems associated with the subject by applying the knowledge acquired.		B31
RA10H-Know, analyse, synthesise and apply the contents, fundamental concepts and applications of the subject.		B32
RA11H-Develop both individual and group work		B33
RA12H-Handle bibliographic material and computer resources.		B34
RA13H-Handle with ease the tools, techniques, equipment and/or material/instrumental of each subject.		B35
RA14H-Use information and communication technology (ICT) tools necessary for the exercise of their profession and for lifelong learning.		B36
RA16X-Produce a report in a rigorous and systematic way.			C14

Topic	Sub-topic
Lesson 1.- Circular Functions. Formulas	1.1. Basic definitions and relationships 1.2. Graphical representations 1.3. Usual formulas 1.4. Inverse functions 1.5. Trigonometric equations
Lesson 2.- Planar Trigonometry. Solving Triangles. Applications.	2.1 Definitions 2.2. Laws of sines and cosines. other formulas 2.3. Solving Oblique Triangles 2.4. Complements and applications
Lesson 3.- Spherical triangles. General Properties.	3.1. Dihedral angles. The supplementary rectilinear 3.2. Trihedron. Polar trihedron 3.3. Spherical surface. Definitions 3.4. Spherical Triangle. Associated trihedron 3.5. Polar Spherical triangle. Properties 3.6. Accessories
Lesson 4.-Groups of Bessel’s formulas. Delambre and Neper analogies.	4.1. Bessel’s formulas 4.2. Briggs' formulas 4.3. Delambre-Gauss' analogies 4.4. Neper’s analogies
Tema 5.- Resolución de Triángulos Esféricos Oblicuángulos.	5.1. Análise de Casos 5.2. Complementos
Lesson 6.- Solving Oblique Spherical Triangles.	6.1. Definitions 6.2. General case: navigating a maximum circumference 6.3. Navegating a parallel 6.4. Navegating a plane 6.5. Estima (estimate position)
Lesson 5.- Solving Right-angled Spherical Triangles.	5.1. Definitions 5.2. Particular formulas. Napier’s nifty Rules 5.3. Particular propierties of the right triangles. 5.4. Solving right triangles. 5.5. Decomposition into right triangles. Perpendicular method.
Lesson 7.- Loci in the Plane. Conic sections.	7.1. Locus in the plane 7.2. Conic sections 7.2.1. Circle 7.2.2. Elipse 7.2.3. Hyperbola 7.2.4. Parabola
Lesson 9.-Loci in the space. Quadric surfaces.	9.1. Loci in the space 9.1.1. Quadric surfaces of revolution 9.1.3. Ruled surfaces 9.2. Particular estudy of Quadric surfaces 9.2.1. Sphere 9.2.2. Ellipsoid 9.2.3. Hyperboloids 9.2.4. Paraboloids 9.2.5. Degenerate quadric surfaces 9.3. General equation of Quadric surfaces 9.3.1. General equation 9.3.2. Invariantes métricos 9.3.3. Clasification 9.4.4. Reduction to Canonical form
Lesson 10.- Functions of several real variables. Limits and Continuity.	10.1.- General definitions 10.2.- Limits 10.3.- Continuity
Lesson 11. Partial and Directional Derivatives. Taylor’s formula. Extrema.	11.1.- Partial derivatives. Tangent plane 11.2.- Directional Derivatives. 11.3.- Higher order Derivatives 11.4.- Taylor’s polinomyal and theorem 11.5.- Relative extrema and conditioned extrema.
Lesson 12.- Integrals in two and three variables. Calculus and applications	12.1.- General definitions 12.2.- Properties 12.3.- Iterated Integrals. Fubini’s Theorem. 12.4.- Change of Variables 12.5.- Applications
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 AII / 2, of the STCW Convention, related to the level of management of chief mates of the Merchant Navy, on ships without gross tonnage limitation and Master up to a maximum of 500 GT.	Table A-II / 2 of the STCW Convention. Mandatory minimum requirements for certification of masters and chief mates on chief on ships of 500 gross tonnage or more.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Guest lecture / keynote speech	A55 A57 B30 B32	30	30	60
Problem solving	A54 B36 B35 B33 B32 B31 B30	24	36	60
Supervised projects	A57 A54 B36 B35 B34 B32 B31 B30 C14	0	10	10
Seminar	A54 A55 B36 B35 B34 B33 B32 B31 B30	0	10	10
Document analysis	A55 A57 B34 B35 B36	0	3	3
Objective test	A54 B30 B31 B32	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
Objective test	Knowledge assessment.

Methodologies	Competencies	Description	Qualification
Objective test	A54 B30 B31 B32	Proba individual de asimilación de coñecementos.	60
Guest lecture / keynote speech	A55 A57 B30 B32	Resolución de cuestións teóricas ou prácticas breves relacionadas cos contidos da sesión maxistral	10
Supervised projects	A57 A54 B36 B35 B34 B32 B31 B30 C14	Realización dos traballos propostos.	15
Problem solving	A54 B36 B35 B33 B32 B31 B30	Capacidade para 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). A student who does not do at least one of hte partial exams or a final exam will be qualified as Not Presented. 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. 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.

Basic	Larson-Hostetler-Edwards (). CÁLCULO (2) . Mac Graw Hill D.G. Zill, W.S. Wright (). Cálculo de Varias Variables. McGraw Hill Elizabeth Vargas, Luis A. Núñez (2020). Geometría III: geometría analítica plana y del espacio. UAPA M.T. Cao Rial, Á. D. Rodríguez Arós (2020). Problemas de Trrigonometría Esférica. Aplicaciones a la navegación. Universidade da Coruña A. R. Arós, F. Blanco, M.J. Muiños (2012). TRIGONOMETRÍA PLANA Y ESFÉRICA CON APLICACIONES A LA NAVEGACIÓN. Paraninfo

Complementary	James Stewart (). CALCULO MULTIVARIABLE. Thomson Editores Vila Mitjá, A. (). ELEMENTOS DE TRIGONOMETRÍA ESFÉRICA. U.P.C. Gutiérrez Gómez-García Castro (). GEOMETRÍA. Pirámide Villa, A. de la (). PROBLEMAS DE ÁLGEBRA LINEAL. Glagsa Swokowski-Kole (). TRIGONOMETRÍA. Thomson Ayres, F. (). TRIGONOMETRÍA PLANA Y ESFÉRICA. Mac Graw Hill

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