Identifying Data 2024/25
Subject (*) Mathematics I Code 771G01005
Study programme
Grao en Enxeñaría de Deseño Industrial e Desenvolvemento do Produto
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 First Basic training 6
Language
Spanish
Galician
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Díaz Díaz, Ana María
 E-mail
ana.ddiaz@udc.es
Lecturers
Baamonde Seoane, María de los Ángeles
Deibe Díaz, Álvaro
Díaz Díaz, Ana María
Orjales Saavedra, Félix
 E-mail
maria.baamonde1@udc.es
alvaro.deibe@udc.es
ana.ddiaz@udc.es
felix.orjales@udc.es
Web http://www.eudi.udc.es
General description A materia aporta aquelas nocións e ferramentas matemáticas que axudan ó alumno a estructurar a súa maneira de pensar e razoar, de modo que sexa capaz de afrontar e resolver con éxito, e de maneira independente, os problemas -novos e distintos- que no desenrolo da súa profesión poida atopar.
O propósito da mateira, por tanto, non é únicamente o de dotar ó alumno de ferramentas matemáticas para a resolución de problemas típicos de cálculo. Mais ben, pretende axudar a desarrollar as capacidades necesarias para estructurar o coñecemento dos problemas, e a maneira de acadar, de forma estructurada, unha solución.

Competencies / Study results
Code Study programme competences / results
A1 Aplicar o coñecemento das diferentes áreas involucradas no Plano Formativo.
A4 Traballar de forma efectiva como individuo e como membro de equipos diversos e multidisciplinares.
A5 Identificar, formular e resolver problemas de enxeñaría.
A6 Formación amplia que posibilite a comprensión do impacto das solucións de enxeñaría nos contextos económico, medioambiental, social e global.
A7 Capacidade para deseño, redacción e dirección de proxectos, en todas as súas diversidades e fases.
A8 Capacidade de usar as técnicas, habilidades e ferramentas modernas para a práctica da enxeñaría.
A9 Capacidade para efectuar decisións técnicas tendo en conta as súas repercusións ou costes económicos, de contratación, de organización ou xestión de proxectos.
A10 Comprensión das responsabilidades éticas e sociais derivadas da súa actividade profesional.
B1 Capacidade de comunicación oral e escrita de maneira efectiva con ética e responsabilidade social como cidadán e como profesional.
B2 Aplicar un pensamento crítico, lóxico e creativo para cuestionar a realidade, buscar e propoñer solucións innovadoras a nivel formal, funcional e técnico.
B4 Traballar de forma colaborativa. Coñecer as dinámicas de grupo e o traballo en equipo.
B5 Resolver problemas de forma efectiva.
B6 Traballar de forma autónoma con iniciativa.
B7 Capacidade de liderado e para a toma de decisións.
B9 Comunicarse de maneira efectiva nun entorno de traballo.
B11 Capacidade de análise e síntese.
B12 Comprensión das responsabilidades éticas e sociales derivadas da súa actividade profesional

Learning aims
Learning outcomes Study programme competences / results
Capacidade para estruturar e dividir problemas complexos plantexados tanto individualmente como en grupo e acadar unha solución empregando tanto ferramentas matemáticas como razoamentos lóxicos e coñecementos de outras áreas A1
A4
A5
A7
A8
 B1
B4
B5
B6
B7
B9
B11
Comprensión da importancia da base matemática presente tanto no deseño como no desenvolvemento de produtos A1
A6
A8
A9
A10
 B2
B5
B11
B12
Coñecemento acerca das curvas en R2 e das súas propiedades: máximos, mínimos, áreas definidas por curvas, etc. Así como do significado asociado os mesmos e da súa utilidade para o deseño. A4
A5
A8
A10
 B5
B11

Contents
Topic Sub-topic
The following blocks or sub-themes develop the contents established in the Verification Report.
 - Introduction
- The real line
- Set of points on the real line
- Limits and continuity of functions
- Derivatives
- Derivable functions
- Local study of a function
- Application of derivatives
- Primitives
- Definite integral
- Application of integrals

Planning
Methodologies / tests Competencies / Results Teaching hours (in-person & virtual) Student’s personal work hours Total hours
Introductory activities A1 A5 A10 A6 A7 A8 B2 B5 B9 B11 B12 1 0 1
Guest lecture / keynote speech A1 A5 A10 A6 A7 A8 B2 B5 B9 B11 B12 28 42 70
Problem solving A1 A5 A6 A7 A9 B1 B2 B5 B6 B7 B9 B11 21 42 63
ICT practicals A1 A4 A5 A6 A7 A8 B1 B2 B4 B5 B6 B7 B9 B11 5.5 5.5 11
Long answer / essay questions A1 A5 A6 A7 B1 B2 B5 B6 B7 B9 B11 2 0 2
 
Personalized attention 3 0 3
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Introductory activities Trátase de unha exposición na aula, interactuando cos alumnos, de aquela información que se considera fundamental para acceder ós coñecementos da asignatura.
Esta exposición interactiva persigue uniformizar os coñecementos mínimos de partida de todolos alumnos, así como obter información do grado de coñecemento de partida dos alumnos para que o profesor poida estructurar con mais eficacia a exposición da materia.
Guest lecture / keynote speech Clases teóricas na aula. Aínda que o propósito fundamental sexa o de impartir os coñecementos teóricos propios da asignatura, habitualmente se utilizarán exemplos a modo de problemas ou exercicios coa finalidade de aclarar aqueles puntos da teoría que se presentan.
Problem solving Clases na aula, cun alto grado de participación (esperada) do alumno, coa finalidade de presentar problemas habituais e familiarizar ó alumno coas pautas de razoamento e os coñecementos necesarios para acadar unha solución.
ICT practicals Uso de ferramentas informáticas específicas relacionadas có modelado e manipulación de curvas en R2 co obxetivo de trasladalas á realidade mediante técnicas de prototipado rápido.
Long answer / essay questions Examen. Xeralmente composto por cuestións prácticas, de exposición que simula unha realidade plausible, que porá a proba o grao de coñecementos acadado á hora de analizar, plantexar e resolver novos problemas.

Personalized attention
Methodologies
ICT practicals
Description
It is fundamentally aimed at helping the student to analyse new problems, to express their characteristics in a language that allows a solution to be reached (using mathematical language) and to solve the problem and understand the final result achieved.
In the ICT practices, tools are presented that help to solve problems. Personalised attention, in this case, aims to show which tools are most appropriate in each case, how to use them, and what can be expected from the results achieved with them. Personalised attention, in the same classroom in which it is given or in the office, aims to resolve any doubts that may arise in this regard.
The solution of problems in the classroom, which also includes their approach and the analysis of the result, is the fundamental part of the knowledge that is intended to be achieved in the subject. In this case, personalised attention is given in the classroom itself, when discussing some standard problems that are posed and solved collectively in the classroom, by the teacher and the group of students.

Assessment
Methodologies Competencies / Results Description Qualification
Long answer / essay questions A1 A5 A6 A7 B1 B2 B5 B6 B7 B9 B11 Exame. Fundamentalmente en forma de exercicios prácticos, que necesitan do coñecemento do total da materia impartida para a súa correcta resolución. 75
ICT practicals A1 A4 A5 A6 A7 A8 B1 B2 B4 B5 B6 B7 B9 B11 Problemas abordados e solucionados utilizando ferramentas das TIC axeitadas a este tipo de problemas. 25
 
Assessment comments

 The assessment will be based on the results of different tests throughout the course, including official exams during assessment periods. 

Students with recognition of part-time dedication and exemption from attendance will be assessed in the same way as the rest of the students. In any case, if any of the placements pose problems of timetable compatibility, a compatible timetable may be agreed with the student. 

ICT placements will only be assessed before the start of the assessment period for first-semester subjects at the first opportunity, and this assessment will be maintained for the second opportunity, if they have to take part in it. 

The calculation of the assessment of the first opportunity will be made according to the following formula: 

First chance mark = practical mark (up to 2.5 out of 10) + continuous assessment mark (up to 2.5 out of 10) + first chance test mark (up to 5 out of 10). 

It is necessary to obtain 30% of the mark assigned to each continuous assessment test in order to pass the subject at the first opportunity.

The second chance assessment includes the part of the subject assessed in the activities carried out throughout the teaching period, except for the ICT practicals. 

The second chance assessment will be calculated according to the following formula: 

Second chance mark = Practicals mark (up to 2.5 out of 10) + second chance test mark (up to 7.5 out of 10). 

Students who sit the advanced assessment will be given the weighted assessment of the previous assessment and may opt for the rest of the mark by means of a mixed or objective test. 

All aspects related to "academic dispensation", "dedication to study", "permanence" and "academic fraud" will be governed in accordance with the current academic regulations of the UDC.

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Sources of information
Basic Víctor Robledo Rella, Antonio Aguilar Gómez, Luis Martínez Arias (2015). Introducción a las matemáticas: Ejercicios y problemas. https://elibro-net.accedys.udc.es/es/ereader/bibliotecaudc/39450?page=1

- Apóstol, T. M. Análisis Matemático. Editorial Reverté, S.A. Barcelona, 1989. This book deals with topics in Higher Calculus. It is aimed at students who are trying to make a transition from elementary calculus to more advanced courses in the theory of real and complex functions. In this case, this text is only recommended so that the EUDI student can revise, if necessary, abstract and specific concepts, which are dealt with in depth here. Particularly noteworthy are the topics dealing with Successions and Numerical Series, and their relationship with Differential and Integral Calculus.

- Ayres, Frank. J.R. and Mendeson, Elliot. Calculus. McGraw-Hill. Colombia, 2000. This is a book aimed at providing a collection of detailed and representative solved problems. Although the major part of the text is made up of its many problems, the fundamental concepts are defined in it, as well as the most important theorems. It is intended as a textbook for higher education calculus courses. Each chapter begins with statements of definitions, principles and theorems. This is followed by solved problems, which form the core of the book. The chapter ends with a group of supplementary unsolved but solved problems. The topics covered in the book go far beyond the scope of this subject.  
  - Demidovich, B. Problemas y Ejercicios de Análisis Matemático. Editorial Paraninfo. Madrid, 1993. This book of Soviet origin, now in its eleventh edition, is a classic of mathematical analysis in engineering schools. It is aimed at students of technical or higher engineering schools. It contains more than 3000 proposed and/or solved problems. It pays special attention to those parts which, because they are more important, require more practice, such as the determination of limits, derivatives, construction of curves, definite and indefinite integrals, series and differential equations. 

 - Diego, Braulio de. Ejercicios de Análisis. Editorial Deimos. Seville, 1983. This is a text aimed at Higher Technical Schools and Science Faculties, and therefore of a more than sufficient level for this subject. It contains a profuse collection of solved problems. The main application for EUDI students may be the calculation of limits of sequences, functions, sums of series and integration. 

 - García, Alfonsa; Villa, Agustín de la; et. al. Cálculo I y II. Editorial Clagsa. Madrid, 1994. Está dirigido a los primeros cursos de Cálculo en estudios de Ciencias o Tecnologías. El primer tomo de este libro aborda el estudio teórico y práctico de la mayoría de los conceptos del Análisis de funciones de una variable. Es, por tanto muy adecuado al temario que se persigue en este caso, por lo que es el libro de texto recomendado para esta materia. Por otra parte, este libro contiene también una importante colección de problemas resueltos y propuestos. Contiene cada tema, además, un interesante test de auto evaluación con el que los estudiantes pueden contrastar sus conocimientos teóricos. 
 - Spiegel, Murray R. Higher Calculus. McGraw-Hill. Madrid 1991. This text can be used as a supplement to the course notes. As in the previous cases, it covers all the concepts of the course syllabus. Each chapter begins with a clear statement of the definitions, principles and theorems, accompanied by abundant illustrative and descriptive material; each chapter ends with a series, graded in difficulty, of solved and proposed problems. The solved problems illustrate the theory and focus on the aspects without whose knowledge the student feels insecure. In the topics that allow it, there are some problems that illustrate the physical applications of the theoretical concepts, a very desirable point in a Technical School. Particularly noteworthy (for this course) are the topics dealing with the calculation of lengths, surfaces and volumes. 
Complementary Lucía Agud Albesa, Margarita Mora Carbonell (2019). Matemáticas básicas para ingenierías: ejercicios resueltos (2ª ed). https://elibro-net.accedys.udc.es/es/ereader/bibliotecaudc/118553


Recommendations
Subjects that it is recommended to have taken before

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus
Mathematics II/771G01006
Statistics/771G01007

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.