Competencies / Study results |
Code
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Study programme competences / results
|
A1 |
Capacidad para plantear y resolver los problemas matemáticos que puedan plantearse en el ejercicio de la profesión. En particular, conocer, entender y utilizar la notación matemática, así como los conceptos y técnicas del álgebra y del cálculo infinitesimal, los métodos analíticos que permiten la resolución de ecuaciones diferenciales ordinarias y en derivadas parciales, la geometría diferencial clásica y la teoría de campos, para su aplicación en la resolución de problemas de Ingeniería Civil. |
B1 |
Que los estudiantes hayan demostrado poseer y comprender conocimientos en un área de estudio que parte de la base de la educación secundaria general, y se suele encontrar a un nivel que, si bien se apoya en libros de texto avanzados, incluye también algunos aspectos que implican conocimientos procedentes de la vanguardia de su campo de estudio |
B2 |
Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio |
B3 |
Que los estudiantes tengan la capacidad de reunir e interpretar datos relevantes (normalmente dentro de su área de estudio) para emitir juicios que incluyan una reflexión sobre temas relevantes de índole social, científica o ética |
B4 |
Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado |
B5 |
Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía |
B6 |
Resolver problemas de forma efectiva. |
B7 |
Aplicar un pensamiento crítico, lógico y creativo. |
B10 |
Comunicarse de manera efectiva en un entorno de trabajo. |
B15 |
Claridad en la formulación de hipótesis. |
B16 |
Capacidad de autoaprendizaje mediante la inquietud por buscar y adquirir nuevos conocimientos, potenciando el uso de las nuevas tecnologías de la información y así poder enfrentarse adecuadamente a situaciones nuevas. |
B18 |
Capacidad para aplicar conocimientos básicos en el aprendizaje de conocimientos tecnológicos y en su puesta en práctica. |
B19 |
Capacidad de realizar pruebas, ensayos y experimentos, analizando, sintetizando e interpretando los resultados. |
C1 |
Expresarse correctamente, tanto de forma oral como por escrito, en las lenguas oficiales de la comunidad autónoma. |
C2 |
Dominar la expresión y la comprensión de forma oral e escrita de un idioma extranjero. |
C3 |
Utilizar las herramientas básicas de las tecnologías de la información y las comunicaciones (TIC) necesarias para el ejercicio de su profesión y para el aprendizaje a lo largo de la vida. |
C4 |
Desarrollarse para el ejercicio de una ciudadanía abierta, culta, crítica, comprometida, democrática y solidaria, capaz de analizar la realidad, diagnosticar problemas, formular e implantar soluciones basadas en el conocimiento y orientadas al bien común. |
C6 |
Valorar críticamente el conocimiento, la tecnología y la información disponible para resolver los problemas con que deben enfrentarse. |
Learning aims |
Learning outcomes |
Study programme competences / results |
To know and understand the theory of Infinitesimal Calculus. |
A1
|
B1
|
C3
|
To know, understand and use mathematical notation. |
A1
|
B1
|
C3
|
To improve mathematical reasoning ability by acquiring or developing different skills: to operate, simplify, clear, relate, distinguish, deduce, demonstrate. |
A1
|
B2 B3 B6 B7 B15
|
C6
|
To solve mathematical problems applying the theory of Infinitesimal Calculus. |
A1
|
B2 B3 B6 B7 B15 B16 B18
|
C6
|
To acquire an analytical attitude towards the different problems that arise, both in the current studies and in the future exercise of the profession. |
|
B3 B6 B7 B19
|
C3 C4 C6
|
To learn to make decisions, studying and reflecting previously. |
|
B2 B3 B5
|
C4 C6
|
To improve the oral and written expression, to be able to transmit information clearly and rigorously. |
|
B4 B7 B10
|
C1 C2
|
Contents |
Topic |
Sub-topic |
I. THE REAL NUMBER. |
1. Introduction. Necessary and sufficient condition.
2. Successive extensions of the concept of number.
3. Field structure. Ordered field.
4. Sequences in Q.
5. Properties of Q.
6. Extension of Q. The real numbers.
7. Properties of R.
8. Operations in R. |
II. METRIC SPACES. |
1. Distance.
2. Balls and neighborhoods
3. Notable points in a metric space.
4. Notable sets in a metric space.
5. Closed, open and compact sets.
6. The metric space (R,||). |
III. NUMERICAL SEQUENCES. |
1. Definition; limit concept; types of successions.
2. Properties of limits.
3. Monotone sequences.
4. Operations with limits. Types of indeterminacy.
5. Convergence criteria.
6. Infinites and infinitesimals.
7. Equivalent sequences.
8. Substitution by equivalent sequences.
9. Calculation of limits. |
IV. FUNCTIONS IN R. |
A. GENERAL NOTIONS
1. Concept of function.
2. Operations with functions.
3. Types of functions.
B. FUNCTION LIMITS
1. Limit of a function.
2. One-side limits.
3. Extension of the concept of limit.
4. Sequential limit.
5. Properties of limits.
6. Operations with limits.
7. Infinites and infinitesimals.
8. Equivalent functions at a point.
9. Substitution by equivalent functions.
C. CONTINUITY OF FUNCTIONS
1. Continuous function.
2. One-sided continuity.
3. Discontinuities.
4. Operations with continuous functions.
5. Continuity of the elementary functions.
6. Composition of continuous functions.
7. Theorems of the continuous functions.
8. Uniform continuity.
D. DIFFERENTIABILITY OF FUNCTIONS
1. Derivability and differentiability.
2. The chain rule. Applications.
3. Derivative of the inverse function.
4. Mean value theorems: Rolle, Cauchy, Lagrange.
5. The derivative as a limit of derivatives.
6. L'Hôpital rules.
7. Successive derivatives.
8. Taylor and McLaurin polynomials.
9. Representation of curves. |
V. CALCULUS OF PRIMITIVES. |
1. Logarithms and hyperbolic functions.
2. Primitive of a function. immediate integrals.
3. Primitive calculation methods: semi-immediate; change of variables; parts; reduction formulas; rational; trigonometric; irrational. |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Laboratory practice |
A1 B10 B15 B1 B2 B3 B4 B6 B7 B18 B19 C1 C2 C6 |
31 |
31 |
62 |
Objective test |
A1 B1 B2 B3 B7 C1 |
1 |
0 |
1 |
Mixed objective/subjective test |
A1 B15 B1 B2 B3 B6 B7 C1 C2 |
2.5 |
0 |
2.5 |
Guest lecture / keynote speech |
A1 B10 B15 B1 B2 B3 B4 B7 C1 C2 C4 C6 |
26 |
26 |
52 |
Problem solving |
A1 B15 B1 B2 B3 B6 B7 B16 B19 C1 C4 C6 |
0 |
12.5 |
12.5 |
Introductory activities |
A1 B1 B2 B6 B7 C3 |
0 |
4 |
4 |
Workbook |
A1 B1 B3 B5 B16 B18 C3 |
0 |
15 |
15 |
|
Personalized attention |
|
1 |
0 |
1 |
|
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies |
Methodologies |
Description |
Laboratory practice |
The Practice lessons are participatory problem-solving sessions. The problems to be solved are published in advance on the web page of the subject. |
Objective test |
The Control Exercises are brief exercises with theoretical and/or practical content. They are carried out in the classroom without prior notice or fixed frequency, in order to check the assimilation of concepts. These exercises can be true/false or multiple choice, questions or short problems. They are marked by the lecturer. |
Mixed objective/subjective test |
The Final Examination of the subject has the form of a mixed test: it is made up of some (or all) of the following parts: a test, short theoretical-practical questions, integration exercises, problem solving. |
Guest lecture / keynote speech |
In the Theory Classes, the theoretical contents of the subject are exposed, accompanied by examples. They are followed by a time dedicated to clarifying doubts, individually or in groups. |
Problem solving |
During the development of each unit, or after finishing it, it is proposed to carry out various activities (Voluntary Exercises). These exercises are solved individually outside the classroom and are collected on dates announced in advance. Some of these exercises may consist of the presentation in public of a section of the syllabus or the resolution of a mathematical problem in public.
The delivery of these exercises is not an essential requirement to pass the subject, but it is recommended for its usefulness to assimilate its contents. It can mean an increase in the final grade, as it is clarified in the Evaluation section. |
Introductory activities |
During the first two weeks of the course, students must solve Practice 0, that can be obtained on the web page of the subject. The solution can be consulted later on the same web page. |
Workbook |
Before beginning the study of each of the units of the subject, it is recommended to access the Mathematics Precourse.
This Precourse is made up of some theory notes, solved and proposed problems and contains basic knowledge to study the subject, which is assumed to have been acquired in previous courses. It has been prepared by various first-year Mathematics professors of this university, from the High School programs.
The basic material provided must be studied, personally solving the proposed exercises, as a guarantee that the knowledge required for the new subject is possessed.
Likewise, during the development of each of the 5 units that make up the subject, it is necessary to study the complementary material that appears in the Support Documents section of the website. |
Personalized attention |
Methodologies
|
Problem solving |
Laboratory practice |
Guest lecture / keynote speech |
|
Description |
For the correct assimilation of the contents developed in the theory classes (lectures) and in the problem classes (laboratory practices) it is highly recommended to consult with the lecturer any doubts that arise, either during said classes or during the personal study of the subject. Doubts that arise during the personal resolution of voluntary surrender problems can also be consulted in the personalized attention interviews.
These consultations will preferably take place at two times:
a) In the classroom, during the 10 minutes after each class.
b) In the lecturer's office during the hours established for this activity.
It is also possible to make inquiries at any time via email, although this means may not be suitable for resolving certain types of doubts, due to its complexity. |
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Problem solving |
A1 B15 B1 B2 B3 B6 B7 B16 B19 C1 C4 C6 |
Carrying out the Voluntary Exercises is valued up to a maximum of 5 points.
Both in the January and July opportunities, these points are added to the overall mark, as long as a minimum score of 45 out of 100 is achieved between the Control Exercises and the Final Exam. |
0 |
Objective test |
A1 B1 B2 B3 B7 C1 |
The Control Exercises have a weight of 20% of the overall mark, both in the January opportunity and in the July one. |
20 |
Mixed objective/subjective test |
A1 B15 B1 B2 B3 B6 B7 C1 C2 |
The Final Exam has a weight of 80% of the overall grade, both in the January and July opportunities. |
80 |
|
Assessment comments |
Both in January and July, the subject can be passed in one of the following ways: a) Obtaining 50 points or more as the sum of the Final Exam mark (out of 80) plus the average mark of the Control Exercises (out of 20) and -if applicable- the mark of the Voluntary Exercises (out of 5). b) Obtaining a grade of 40 out of 80 in the Final Exam. Voluntary Exercises are not taken into account in this option. 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.
|
Sources of information |
Basic
|
Estela, M.R.; Sáa, J. (2008). Cálculo con soporte interactivo en Moodle. Pearson-Prentice Hall, Madrid
García, A. y otros (1998). Cálculo I. Teoría y problemas de Análisis Matemático en una variable. CLAGSA, Madrid
Granero, F. (2001). Cálculo Integral y aplicaciones. Prentice Hall; Madrid
Estela, M.R.; Serra, A.M. (2008). Cálculo. Problemas resueltos. Pearson-Prentice Hall, Madrid
Franco, J.R. (2003). Introducción al Cálculo. Problemas y ejercicios resueltos. Prentice Hall, Madrid |
For the preparation of the subject it is important to have the following material, which is available on the website: 1. Mathematics Precourse. 2. Detailed program. 3. Course notes -which include tests and self-assessment questions- and other supporting documents. 4. Practice and integrals exercises. In addition to the above, depending on the needs, it will be useful to consult some of the texts of the bibliography, basic or complementary, that can be obtained in the Faculty Library. |
Complementary
|
Tébar, E. y Tébar M.A. (1991). 909 problemas de Cálculo Integral (2 tomos) . Tébar Flores, Madrid
Burgos, J (2006). Cálculo Infinitesimal de una variable. Madrid, Mc Graw-Hill
Granero, F. (1995). Cálculo Infinitesimal. Una y varias variables. Mc Graw-Hill, Madrid
Granero, F. (1991 ). Ejercicios y problemas de Cálculo (2 tomos) . Tébar Flores, Albacete |
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Recommendations |
Subjects that it is recommended to have taken before |
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Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
Cálculo infinitesimal II/632G02002 | Ecuacións diferenciais/632G02017 |
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