Identifying Data 2022/23
Subject (*) Mathematics III Code 631G02260
Study programme
Grao en Tecnoloxías Mariñas
Descriptors Cycle Period Year Type Credits
Graduate 2nd four-month period
 Second Basic training 6
Language
Spanish
Galician
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Cao Rial, María Teresa
 E-mail
teresa.cao@udc.es
Lecturers
Cao Rial, María Teresa
 E-mail
teresa.cao@udc.es
Web
General description Impartiranse os métodos básicos do Cálculo Numérico e da Estatística realizando prácticas en computador (co programa Octave), proporcionando así unha ferramenta que poida ser útil tanto na actual vida académica como na futura vida profesional.

Study programme competencies
Code Study programme competences
A12 CE12 - Interpretar e representar correctamente o espazo tridimensional, coñecendo os obxectivos e o emprego dos sistemas de representación gráfica.
A14 CE14 - Avaliación cualitativa e cuantitativa de datos e resultados, así como a representación e interpretación matemáticas de resultados obtidos experimentalmente.
A17 CE17 - Modelizar situacións e resolver problemas con técnicas ou ferramentas físico-matemáticas.
A18 CE18 - Redacción e interpretación de documentación técnica.
B1 CT1 - Capacidad para gestionar los propios conocimientos y utilizar de forma eficiente técnicas de trabajo intelectual
B2 CT2 - Resolver problemas de forma efectiva.
B3 CT3 - Comunicarse de xeito efectivo nun ámbito de traballo.
B4 CT4 - Traballar de forma autónoma con iniciativa.
B5 CT5 - Traballar de forma colaboradora.
B6 CT6 - Comportarse con ética e responsabilidade social como cidadán e como profesional.
B7 CT7 - Capacidade para interpretar, seleccionar e valorar conceptos adquiridos noutras disciplinas do ámbito marítimo, mediante fundamentos físico-matemáticos.
B8 CT8 - Versatilidade.
B9 CT9 - Capacidade para a aprendizaxe de novos métodos e teorías, que lle doten dunha gran versatilidade para adaptarse a novas situacións.
B10 CT10 - Comunicar por escrito e oralmente os coñecementos procedentes da linguaxe científica.
B11 CT11 - Capacidade para resolver problemas con iniciativa, toma de decisións, creatividade, razoamento crítico e de comunicar e transmitir coñecementos habilidades e destrezas.
C1 C1 - Expresarse correctamente, tanto de forma oral coma escrita, nas linguas oficiais da comunidade autónoma.
C2 C2 - Dominar a expresión e a comprensión de forma oral e escrita dun idioma estranxeiro.
C3 C3 - Utilizar as ferramentas básicas das tecnoloxías da información e as comunicacións (TIC) necesarias para o exercicio da súa profesión e para a aprendizaxe ao longo da súa vida.
C4 C4 - Desenvolverse para o exercicio dunha cidadanía aberta, culta, crítica, comprometida, democrática e solidaria, capaz de analizar a realidade, diagnosticar problemas, formular e implantar solucións baseadas no coñecemento e orientadas ao ben común.
C5 C5 - Entender a importancia da cultura emprendedora e coñecer os medios ao alcance das persoas emprendedoras.
C6 C6 - Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse.
C7 C7 - Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida.
C8 C8 - Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade.
C9 CB1 - Demostrar que posúen e comprenden coñecementos na área de estudo que parte da base da educación secundaria xeneral, e que inclúe coñecementos procedentes da vanguardia do seu campo de estudo
C10 CB2 - Aplicar os coñecementos no seu traballo ou vocación dunha forma profesional e poseer competencias demostrables por medio da elaboración e defensa de argumentos e resolución de problemas dentro da área dos seus estudos
C11 CB3 - Ter a capacidade de reunir e interpretar datos relevantes para emitir xuicios que inclúan unha reflexión sobre temas relevantes de índole social, científica ou ética
C12 CB4 - Poder transmitir información, ideas, problemas e solucións a un público tanto especializado como non especializado.
C13 CB5 - Ter desenvolvido aquelas habilidades de aprendizaxe necesarias para emprender estudos posteriores con un alto grao de autonomía.

Learning aims
Learning outcomes Study programme competences
A12
A14
A17
A18
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B11
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13

Contents
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.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Collaborative learning A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 2 15 17
ICT practicals A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 14 25 39
Problem solving A12 A14 A17 A18 B1 B2 B3 B4 B5 B7 B8 B9 B10 B11 C1 C2 C3 C6 C7 C8 C10 C11 C12 C13 14 25 39
Guest lecture / keynote speech A12 A14 A17 A18 B1 B3 B4 B6 B7 B9 B10 B11 C1 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 20 10 30
Objective test A12 A14 A17 A18 B1 B2 B4 B6 B7 B10 B11 C1 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 4 0 4
Online discussion A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C4 C5 C6 C7 C8 C10 C11 C12 0 10 10
Document analysis A12 A14 A17 A18 B1 B4 B5 B7 B9 C1 C2 C3 C4 C5 C6 C7 C8 C11 0 5 5
 
Personalized attention 6 0 6
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Collaborative learning Traballo en grupo
ICT practicals Prácticas na Aula de Informática cos programas Matlab e Calc
Problem solving Resolver problemas propostos
Guest lecture / keynote speech Exposición inicial de cada tema
Objective test Proba individual de coñecementos adquiridos
Online discussion Participación nos foros abertos en Moodle
Document analysis Valoración da información obtida en libros e internet

Personalized attention
Methodologies
Problem solving
ICT practicals
Description
The students are encouraged to attend in small groups or individually to the professors' office, or by TEAMS, to solve questions that may arise, thus obtaining a more specific guidance, acoording to their specific difficulties.

Assessment
Methodologies Competencies Description Qualification
Problem solving A12 A14 A17 A18 B1 B2 B3 B4 B5 B7 B8 B9 B10 B11 C1 C2 C3 C6 C7 C8 C10 C11 C12 C13 Plantexar os problemas que logo se resolverán coas TIC.
 10
Guest lecture / keynote speech A12 A14 A17 A18 B1 B3 B4 B6 B7 B9 B10 B11 C1 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 Asistencia e participación nas clases teóricas.
 5
Collaborative learning A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 Realización de traballos grupais
 9
ICT practicals A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 Realización das prácticas propostas na aula de Informática.
 45
Objective test A12 A14 A17 A18 B1 B2 B4 B6 B7 B10 B11 C1 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 Resposta sobre os coñecementos adquiridos.
 30
Online discussion A12 A14 A17 A18 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 C1 C3 C4 C5 C6 C7 C8 C10 C11 C12 Participación nos debates abertos no Campus Virtual.
 1
 
Assessment comments

Students who participate in the EHEA system must attend a minimum of 80% of the total classes. Continuous evaluation gives 70% of the final marks, and throughout the course there will be partial tests that grant the remaining 30%.

Students who passed the continuous evaluation but failed to pass the partial tests, will have the opportunity to achieve the remaining 30% of the final marks in a final exam of the whole subject, at first or second opportunity.

Students who decide NOT to participate in the EHEA system will be evaluated through two tests. The first test is devoted to questions of theoretical-practical knowledge and problem solving,  and provides 30% of the final marks. The second test concerns the implementation of some of the numerical methods studied in the course, and provides the remaining 70% of the final marks.

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 graduate 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. 

Fraudulent conduct in tests or activities, once verified, will cause a final mark of 0, invalidating any mark obtained in the in previous activities, as established in the current academic regulations at UDC.

Sources of information
Basic Curtis F. Gerald (1991). Análisis Numérico. Alfaomega
Burden-Faires (1998). Análisis Numérico. Thomson
García Merayo-Nevot Luna (1992). Análisis Numérico. Paraninfo
Spiegel (1991). Estadística. McGraw-Hill
J.M. Viaño (1995). Lecciones de Métodos Numéricos Vol 1: Introducción general y análisis de errores. Tórculo Edicións
J.M. Viaño (1997). Lecciones de Métodos Numéricos Vol 2: Resolución de ecuaciones numéricas. Tórculo Edicións
J.M. Viaño, M. Burgurea (1999). Lecciones de Métodos Numéricos Vol 3: Interpolación. Tórculo Edicións
Huerta-Sarrate-Rodríguez Ferrán (1998). Métodos Numéricos. Edicions UPC
Mathews-Fink (1999). Métodos Numéricos con Matlab. Prentice Hall
Cordero-Hueso-Martínez-Torregrosa (2005). Métodos Numéricos con Matlab. Universidad Politécnica de Valencia
S. C. Chapra, R. P. Canale (2015). Métodos Numéricos para Ingenieros. Mc-Graw-Hill
Michavila-Gavete (1992). Programación y Cálculo Numérico. Reverté

Complementary


Recommendations
Subjects that it is recommended to have taken before
Mathematics I/631G02151
Informatics/631G02154
Mathematics II/631G02156

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus

Other comments


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.