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Teaching GuideTerm Higher Technical University College of Nautical Science and Naval Engines |
| Grao en Náutica e Transporte Marítimo |
 Subjects |
| Mathematics II |
| Contents |
| Identifying Data | 2020/21 | |||||||||||||
| Subject | Mathematics II | Code | 631G01106 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | Basic training | 6 | ||||||||||
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| 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. Circular 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.- Double integrals. 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 |
| Lesson 13.- Triple Integrals. Calculus and applications. | 13.1.- General definitions 13.2.- Properties 13.3.- Iterated Integrals. Fubini’s Theorem 13.4.- Change of Variables 13.5.- Applications |
| Lesson 14.- First order Differential Equations. | 14.1.- General definitions 14.2.- First order Differential Equations. 14.3.- Special cases of first order ODEs |
| Lesson 15.- High order Differential Equations. | 15.1.- Homogeneous and Nonhomogeneous Second Order EDO’s 15.2.- Higher order linear equations with constant coefficients 15.3.- Higher order Nonhomogeneous equations |
| Lesson 16.- Systems of Differential Equations. | 16.1.- Systems of Ordinary Differential Equations. 16.2.- Systems of Linear Differential Equations with constant coefficients. |
| 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. |
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