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Teaching GuideTerm Higher Technical University College of Nautical Science and Naval Engines |
| Grao en Tecnoloxías Mariñas |
 Subjects |
| Mathematics III |
| Contents |
| Identifying Data | 2022/23 | |||||||||||||
| Subject | Mathematics III | Code | 631G02260 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
Second | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
| Lesson 1.- Introduction to MATLAB and Octave |
1.1.- Types of data. Basic operations. 1.2.- Vectors and matrices 1.3.- Functions 1.4.- Logical operators |
| Lesson 2.- Number, Algorithm and Errors |
2.1.- Introduction 2.2.- Numbers: Representation and Storage 2.3.- Algorithms 2.4.- Errors: Classification and Propagation |
| Lesson 3.- Numerical Solution of Systems of Linear Equations |
3.1.- General considerations 3.2.- Direct methods 3.2.1.- Systems with Immediate Solution 3.2.1.1.- Diagonal matrix 3.2.1.2.- Upper Triangular matrix 3.2.1.2.- Inferior Triangular matrix 3.2.2.- Methods of Elimination or Transformation 3.2.2.1.- Method of Gauss 3.2.2.1.- Method of Gauss-Jordan 3.2.3.- Methods of Decomposition: Factorisation LU 3.2.3.1.- Method of Doolittle 3.2.3.2.- Method of Crout 3.2.3.3.- Method of Cholesky 3.3.- Iterative methods 3.3.1.- Method of Jacobi 3.3.2.- Method of Gauss-Seidel |
| Lesson 4.- Numerical Interpolation |
4.1.- Introduction 4.2.- Lagrange Interpolating Polynomial 4.3.- Hermite Interpolating Polynomial 4.4.- Divided Differences. Newton Formula |
| Lesson 5.-Numerical solution of nonlinear equations |
5.1.- Introduction 5.2.- Method of the Bisection 5.3.- Method of Newton-Raphson 5.4.- Method of the Secante. It regulates Falsi. 5.5.- Method of the Fixed Point |
| Lesson 6.- Numerical Differentiation and Numerical Integration |
6.1.- Finite differences. Derivación Numerical. 6.2.- Numerical integration. General concepts. 6.3.- Rectangular approximations 6.4.- Method of the Trapezes 6.5.- Rule of Simpson 6.6.- Formulas of Quadrature |
| Lesson 7.- Numerical Solution of Ordinary Differential Equations | 7.1.- Introduction: General Definitions 7.2.- Methods of Taylor 7.3.- Method of Euler 7.4.- Method of Heun 7.5.- Methods of Runge-Kutta |
| Lesson 8.- Statistics Methods |
8.1 Descriptive Statistics 8.1.1 Generalities 8.1.2 Treatment of the information and graphic representations 8.1.3 Measures of centralisation. Measures of dispersion 8.1.4 Binomial and Normal Distributions 8.2 Curve Adjustment 8.2.1 Linear Regression. 8.2.2 Least Squares Method 8.2.3 Measures of Accuracy 8.2.4 Nonlinear Measures of Accuracy |
| 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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