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Teaching GuideTerm Higher Technical University College of Nautical Science and Naval Engines |
| Grao en Tecnoloxías Mariñas |
 Subjects |
| Mathematics II |
| Contents |
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| Identifying Data | 2022/23 | |||||||||||||
| Subject | Mathematics II | Code | 631G02156 | |||||||||||
| 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 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. |
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