1. General information
Course:
CALCULUS I
Code:
56301
Type:
BASIC
ECTS credits:
6
Degree:
351 - UNDERGRADUATE DEGREE PROG. IN MECHANICAL ENGINEERING (ALM)
Academic year:
2020-21
Center:
106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING
Group(s):
55
56
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
Spanish
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
CARLOS FUNEZ GUERRA
- Group(s):
55
Building/Office
Department
Phone number
Email
Office hours
Despacho 2.09 - Edificio E¿lhuyar
MATEMÁTICAS
6049
carlos.funez@uclm.es
Lecturer:
PEDRO JOSE MORENO GARCIA
- Group(s):
56
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
6049
PedroJose.Moreno@uclm.es
Lecturer:
DOROTEO VERASTEGUI RAYO
- Group(s):
55
56
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
926052122
doroteo.verastegui@uclm.es
2. Pre-Requisites
In order to achieve the learning objectives of the subject, knowledge and skills that have been guaranteed in pre-university training are required. In particular, he will learn the knowledge of geometry and basic trigonometry, elementary mathematical operations (powers, logarithms, fractions) and the fundamentals of graphic representation of functions. With regard to the basic skills in the handling of instruments is the elementary management of computers: access, file management, folders, etc.
3. Justification in the curriculum, relation to other subjects and to the profession
The industrial engineer uses the knowledge of Physics, Mathematics and engineering techniques to develop his professional activity in aspects such as control, instrumentation and automation of processes and equipment, as well as the design, construction, operation and maintenance of industrial products. . This training allows you to participate successfully in the different branches that integrate industrial engineering, such as mechanics, electricity, electronics, etc., adapt to the changes of technologies in these areas and, where appropriate, generate them, thus responding to needs that arise in the productive and service branches to achieve the well-being of the society to which it is owed.
4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| A01 | To understand and have knowledge in an area of study that moves on from the general education attained at secondary level and usually found at a level that, while supported in advanced text books, also includes some aspects that include knowledge found at the cutting edge of the field of study. |
| A02 | To know how to apply knowledge to work or vocation in a professional manner and possess the competences that are usually demonstrated by the formulation and defence of arguments and the resolution of problems in the field of study. |
| A03 | To have the capability to gather and interpret relevant data (normally within the area of study) to make judgements that include a reflection on themes of a social, scientific or ethical nature. |
| A07 | Knowledge of Information Technology and Communication (ITC). |
| A08 | Appropriate level of oral and written communication. |
| A12 | Knowledge of basic materials and technologies that assist the learning of new methods and theories and enable versatility to adapt to new situations. |
| A13 | Ability to take the initiative to solve problems, take decisions, creativity, critical reasoning and ability to communicate and transmit knowledge, skills and abilities in Mechanical Engineering. |
| A17 | Ability to apply principles and methods of quality control. |
| B01 | Ability to solve mathematical problems that occur in engineering. Aptitude to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimization. |
| CB01 | Prove that they have acquired and understood knowledge in a subject area that derives from general secondary education and is appropriate to a level based on advanced course books, and includes updated and cutting-edge aspects of their field of knowledge. |
| CB02 | Apply their knowledge to their job or vocation in a professional manner and show that they have the competences to construct and justify arguments and solve problems within their subject area. |
| CB03 | Be able to gather and process relevant information (usually within their subject area) to give opinions, including reflections on relevant social, scientific or ethical issues. |
| CB04 | Transmit information, ideas, problems and solutions for both specialist and non-specialist audiences. |
| CB05 | Have developed the necessary learning abilities to carry on studying autonomously |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| To know the tundamentals and applications of Optimization | |
| Know the main approaches for resolution through using numerical methods, to use some statistical software packages at user level, data processing, mathematical calculus and vizualization, set out algorithms and program through programming language of a high level, vizualize functions, geometric figures and data, design experiments, analyze data and interpret results | |
| Know the use of the functions of one and various variables including its derivation, integration and graphic representation | |
| Be familiar with the concepts of differential geometry and use them appropriately. | |
| Additional outcomes | |
| Description | |
6. Units / Contents
-
Unit 1: Elemmental concepts. Elemental functions. Limits and continuity
-
Unit 2: Differential calculus
-
Unit 3: Integral calculus
-
Unit 4: Introduction to ordinary differential equations
7. Activities, Units/Modules and Methodology
| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
| Class Attendance (theory) [ON-SITE] | Combination of methods | A01 A02 A03 A07 A12 B01 CB01 CB02 CB03 CB04 CB05 | 1 | 25 | N | N | ||
| Individual tutoring sessions [ON-SITE] | Problem solving and exercises | A01 A02 A03 A08 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 | 0.2 | 5 | N | N | ||
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | A02 A07 A13 B01 CB01 CB02 CB03 CB04 CB05 | 0.6 | 15 | Y | N | ||
| Workshops or seminars [ON-SITE] | Problem solving and exercises | A02 A08 A12 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 | 0.1 | 2.5 | N | N | ||
| Computer room practice [ON-SITE] | Practical or hands-on activities | A02 A07 B01 CB01 CB02 CB03 CB04 CB05 | 0.3 | 7.5 | Y | N | ||
| Final test [ON-SITE] | Assessment tests | A01 A02 A03 A07 A08 A12 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 | 0.2 | 5 | Y | Y | ||
| Other off-site activity [OFF-SITE] | Self-study | A02 A03 A08 B01 CB01 CB02 CB03 CB04 CB05 | 3.6 | 90 | N | N | ||
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
| Total credits of out of class work: 3.6 | Total hours of out of class work: 90 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
8. Evaluation criteria and Grading System
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Final test | 70.00% | 70.00% | Final test with teorical questions and problems. |
| Progress Tests | 20.00% | 20.00% | For the evaluation of the academic works carried out by the students in class, a memory should be given where the approach of the problem will be assessed, the use of appropriate terminology and notation to express the mathematical ideas and relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleaning and presentation of the document. |
| Assessment of problem solving and/or case studies | 5.00% | 5.00% | For the evaluation of the practices in the computer room, with application of specific software, the delivery of the work carried out in the same ones and a documentation with the resolution of the same will be valued. |
| Assessment of activities done in the computer labs | 5.00% | 5.00% | Finally, there will be a written test that will consist of questions, theoretical questions and problems whose evaluation criteria will be similar to those of the academic works described above. |
| Total: | 100.00% | 100.00% |
According to art. 4 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 12.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).
Evaluation criteria for the final exam:
-
Continuous assessment:In order to obtain the final grade, the 3 evaluation systems described are computed, with the specified weights, and a grade equal to or greater than 4 points out of 10 must be obtained in the final written test. If the grade obtained in said test was less than 5 points, it will be considered as the final grade of the subject.
-
Non-continuous evaluation:Evaluation criteria not defined
Specifications for the resit/retake exam:
There will be a final written test, whose weight will be 100% of the global grade of the subject and which will consist of questions, theoretical issues and problems where the approach of the subject or problem will be assessed, the use of terminology and appropriate notation to express the ideas and mathematical relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleanliness and presentation of the document.
Specifications for the second resit / retake exam:
There will be a final written test, whose weight will be 100% of the global grade of the subject and which will consist of questions, theoretical issues and problems where the approach of the subject or problem will be assessed, the use of terminology and appropriate notation to express the ideas and mathematical relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleanliness and presentation of the document.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Individual tutoring sessions [PRESENCIAL][Problem solving and exercises] | 5 |
| Workshops or seminars [PRESENCIAL][Problem solving and exercises] | 2.5 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 7.5 |
| Final test [PRESENCIAL][Assessment tests] | 5 |
| Unit 1 (de 4): Elemmental concepts. Elemental functions. Limits and continuity | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 3 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Other off-site activity [AUTÓNOMA][Self-study] | 10 |
| Unit 2 (de 4): Differential calculus | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 9 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 5 |
| Other off-site activity [AUTÓNOMA][Self-study] | 30 |
| Unit 3 (de 4): Integral calculus | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 9 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 5 |
| Other off-site activity [AUTÓNOMA][Self-study] | 35 |
| Unit 4 (de 4): Introduction to ordinary differential equations | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 4 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3 |
| Other off-site activity [AUTÓNOMA][Self-study] | 15 |
| Global activity | |
|---|---|
| Activities | hours |
10. Bibliography and Sources
| Author(s) | Title | Book/Journal | Citv | Publishing house | ISBN | Year | Description | Link | Catálogo biblioteca |
|---|---|---|---|---|---|---|---|---|---|
| Algunos recursos en Internet | http://www.calculus.org/ | ||||||||
| Algunos recursos en Internet | http://matematicas.uclm.es/ind-cr/calculoi | ||||||||
| Algunos recursos en Internet | http://www.sosmath.org/calculus/calculus.html | ||||||||
| Algunos recursos en Internet | http://ocw.mit.edu/OcwWeb/Mathematics/index.htm | ||||||||
| Algunos recursos en Internet | http://archives.math.utk.edu/visual.calculus/ | ||||||||
| A. García, A. López, G. Rodríguez, S. Romero, A. de la Villa | Calculo I. Teoría y problemas de funciones en una variable | Madrid | CLAGSA | 84-921847-0-1 | 1996 | ||||
| B. P. Demidovich | 5000 problemas de análisis matemático | Thompson-Paraninfo | 2002 | Libro de problemas | |||||
| B. P. Demidovich | Problemas y ejercicios de análisis matemático | 11 edición, Ed. Paraninfo | 1993 | Libro de problemas | |||||
| C. H. Edwards, D. E. Penney | Cálculo diferencial e integral | Cuarta Edición, Pearson Educación | 1997 | Libro de teoría | |||||
| E. J. Espinosa, I. Canals, M. Meda, R. Pérez, C. A. Ulín | Cálculo diferencial: Problemas resueltos | Reverte | 2009 | Libro de problemas | |||||
| L. S. Salas, E. Hille, G. Etgen | Calculus volumen I: Una y varias variables | Cuarta edición en español, Ed. Reverté | 2002 | Libro de teoría | |||||
| P. Pedregal | Cálculo esencial | ETSI Industriales, UCLM | 2002 | Libro de teoría | |||||
| R. Larson, R.P. Hostetler, B. H. Edwards | Cálculo I | Mc. Graw-Hill Interamericana | 2005 | Libro de teoría | |||||
| T. Apostol | Calculus | Vol. I, Segunda edición, Reverté | 1990 | Libro de teoría |