1. General information
Course:
CALCULUS I
Code:
56301
Type:
BASIC
ECTS credits:
6
Degree:
351 - UNDERGRADUATE DEGREE PROG. IN MECHANICAL ENGINEERING (ALM)
Academic year:
2023-24
Center:
106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING
Group(s):
56
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
Spanish
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
ANGEL ROMERO VILLADA
- Group(s):
56
Building/Office
Department
Phone number
Email
Office hours
MATEMÁTICAS
Angel.Romero@uclm.es
Lecturer:
DOROTEO VERASTEGUI RAYO
- Group(s):
56
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
926052122
doroteo.verastegui@uclm.es
2. Pre-Requisites
For students to achieve the learning objectives described, they must possess knowledge and skills that are supposed to be guaranteed in their training prior to entering the University:
- Knowledge: basic geometry and trigonometry, basic mathematical operations (powers, logarithms, fractions), polynomials, matrices, derivation, integration and graphical representation of functions.
- Basic skills in instrumental management: elementary management of computers.
3. Justification in the curriculum, relation to other subjects and to the profession
The Industrial Engineer is the professional who uses the knowledge of the physical, mathematical and statistical sciences, together with the engineering techniques, to develop his professional activity in aspects such as the 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 successfully participate in the different branches that make up industrial engineering, such as mechanics, electricity, electronics, etc., adapt to changes in technology in these areas and, where appropriate, generate them, responding thus to the needs that arise in the productive and service branches to achieve the well-being of the society to which it is due.
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. |
| 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 use of the functions of one and various variables including its derivation, integration and graphic representation | |
| 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 | |
| Be able to express yourself correctly both orally and in writing, and, in particular, to know how to use mathematical language to express with precision quantities and operations that appear in industrial engineering. Become accustomed to working in a team and behaving respectfully. | |
| Know how functions and data are approximated through development in series of power and Fourier and their applications | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Introduction to Calculus.
-
Unit 2: Real functions of one variable.
-
Unit 3: Derivation.
-
Unit 4: Numerical series and power series.
-
Unit 5: Approximate resolution of equations.
-
Unit 6: Integration.
-
Unit 7: Numerical Integration.
-
Unit 8: Improper Integrals.
-
Unit 9: Numerical Algorithmic.
ADDITIONAL COMMENTS, REMARKS
Practices in the Computer classroom:
Practice 1: Introduction to MATLAB. Mathematical functions with MATLAB.
Practice 2: Basic programming with MATLAB.
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] | Lectures | A01 A02 A03 A07 B01 CB01 CB02 CB03 CB04 CB05 | 1.2 | 30 | N | N | Participatory master lesson, with blackboard and projector cannon. | |
| Problem solving and/or case studies [ON-SITE] | Combination of methods | A02 A07 B01 CB01 CB02 CB03 CB04 CB05 | 0.6 | 15 | Y | N | Solving exercises and problems in the classroom in a participatory way | |
| Class Attendance (practical) [ON-SITE] | Combination of methods | A02 A07 B01 CB01 CB02 CB03 CB04 CB05 | 0.4 | 10 | Y | Y | Performing problems using the use of computer programs | |
| Formative Assessment [ON-SITE] | Assessment tests | A01 A02 A03 A07 A08 A17 B01 CB01 CB02 CB03 CB04 CB05 | 0.2 | 5 | Y | Y | Final evaluation of the subject by written test | |
| Study and Exam Preparation [OFF-SITE] | Self-study | A02 A03 A08 B01 CB01 CB02 CB03 CB04 CB05 | 3.6 | 90 | N | N | Autonomous personal study of the student and supervised work | |
| 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% | 90.00% | Finally, a written test will be carried out that will consist of questions, theoretical questions and problems whose criteria of evaluation will be similar to those of academic papers described above. |
| Progress Tests | 20.00% | 0.00% | For the evaluation of the progress tests carried out by Students will assess the problem statement, the use of appropriate terminology and notation to express the mathematical ideas and relationships used, the choice of 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 activities done in the computer labs | 10.00% | 10.00% | For the evaluation of the practices in the computer room, with specific software application, delivery will be valued of the work carried out in them, having to be defended orally before the teacher. |
| 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:To obtain the final grade, the 3 evaluation systems described are computed, with the specified weights, and must be obtained in the final test.
written a grade equal to or greater than 4 points out of 10.
If the grade obtained in said test is less than 5 points, it will be put as the final grade for the course. -
Non-continuous evaluation:To carry out the non-continuous evaluation, the proposed activities must be delivered during the activities in the computer rooms and a final test will be carried out. If the proposed activities are not delivered, the student must obtain at least 5.6 in the final test to pass the subject.
Specifications for the resit/retake exam:
A final written test will be carried out, the weight of which will be 90% of the overall grade for the subject and will consist of questions, theoretical questions and
problems where the approach to the topic or problem will be assessed, the use of appropriate terminology and notation to express ideas and relationships
mathematics 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. The remaining 10% of the grade corresponds to Matlab practices.
problems where the approach to the topic or problem will be assessed, the use of appropriate terminology and notation to express ideas and relationships
mathematics 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. The remaining 10% of the grade corresponds to Matlab practices.
Specifications for the second resit / retake exam:
A final written test will be carried out, the weight of which will be 90% of the overall grade for the subject and will consist of questions, theoretical questions and
problems where the approach to the topic or problem will be assessed, the use of appropriate terminology and notation to express ideas and relationships
mathematics 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. The remaining 10% of the grade corresponds to Matlab practices.
problems where the approach to the topic or problem will be assessed, the use of appropriate terminology and notation to express ideas and relationships
mathematics 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. The remaining 10% of the grade corresponds to Matlab practices.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 30 |
| Problem solving and/or case studies [PRESENCIAL][Combination of methods] | 15 |
| Class Attendance (practical) [PRESENCIAL][Combination of methods] | 10 |
| Formative Assessment [PRESENCIAL][Assessment tests] | 5 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 90 |
| Global activity | |
|---|---|
| Activities | hours |
| General comments about the planning: | Time planning may undergo some variations depending on the calendar and the needs of the academic course. The dates of the practices will be specified in the first three school weeks. |
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://ocw.mit.edu/OcwWeb/Mathematics/index.htm | ||||||||
| 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://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 | Libro | Madrid | CLAGSA | 84-921847-0-1 | 1996 | Libro de teoría y problemas | ||
| B. P. Demidovich | 5000 problemas de análisis matemático | Libro | Thompson | 2002 | Libro de problemas. | ||||
| B. P. Demidovich | Problemas y ejercicios de análisis matemático | Libro | 11 edición, Ed. Paraninfo | 1993 | Libro de problemas. | ||||
| C. H. Edwards, D. E. Penney | Cálculo diferencial e integral | Libro | Cuarta Edición, Pearson Educación | 1997 | Libro de teoría | ||||
| E. J Espinosa, I. Canals, M. Medea, R. Pérez, C. A. Ulín | Cálculo diferencial: Problemas resueltos | Libro | Reverte | 2009 | Libro de problemas. | ||||
| L. S. Salas, E. Hille, G. Etgen | Calculus Volumen I: Una y varias variables | Libro | Cuarta Edición en español, Ed. Reverté | 2002 | Libro de teoría. | ||||
| P. Pedregal | Cálculo esencial | Libro | ETSI Industriales, UCLM | 12002 | Libro de teoría | ||||
| R. Larson, R.P. Hostetler, B. H. Edwards | Cálculo I | Libro | Mc. Graw-Hill Interamericana | 2005 | Libro de teoría. | ||||
| T. Apostol | Calculus | Libro | Vol. I, Segunda edición, Reverté | 1990 | Libro de teoría. |