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Teaching GuideTerm Higher Technical University College of Nautical Science and Naval Engines |
| Grao en Tecnoloxías Mariñas |
 Subjects |
| Matemáticas II |
| Contents |
| Identifying Data | 2016/17 | |||||||||||||
| Subject | Matemáticas II | Code | 631G02156 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | FB | 6 | ||||||||||
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| Topic | Sub-topic |
| Lesson 1.- Bilinear forms. Quadratic forms. |
1.1.- Bilinear forms. Associated Matrix 1.2.- Symmetrical bilinear forms 1.3.- Quadratic forms 1.4.- Canonical Quadratic form. Reduction to the Canonical Form 1.5.- Classification of the Quadratic Forms |
| 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 |
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