Guías-E

1. General information

Course:

CALCULUS

Code:

19548

Type:

BASIC

ECTS credits:

6

Degree:

384 - MINING AND ENERGY ENGINEERING DEGREE

Academic year:

2023-24

Center:

106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING

Group(s):

51

Year:

1

Duration:

First semester

Main language:

Spanish

Second language:

English

Use of additional languages:

English Friendly:

Y

Web site:

Bilingual:

N

Lecturer: PEDRO JOSE MORENO GARCIA - Group(s): 51

Building/Office

Department

Phone number

Email

Office hours

Elhuyar / Matemáticas

MATEMÁTICAS

6049

PedroJose.Moreno@uclm.es

Lecturer: DOROTEO VERASTEGUI RAYO - Group(s): 51

Building/Office

Department

Phone number

Email

Office hours

Elhuyar / Matemáticas

MATEMÁTICAS

926052122

doroteo.verastegui@uclm.es

To be published at the beginning of the semester

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 Mining Engineer is the professional who uses the knowledge of physical and mathematical sciences and engineering techniques to develop his professional activity in aspects such as the search for mining resources, the exploitation of mines, the extraction of elements of economic interest from their original minerals, the control, instrumentation and automation of processes and equipment, as well as the design, construction, operation and maintenance of extractive industrial processes, etc. This training allows him/her to participate successfully in the different branches that make up mining engineering, to adapt to changes in technologies in these areas and, if necessary, to generate them, thus responding to the needs that arise in the productive and service branches to achieve the welfare of the society to which he/she owes.

Within the MATHEMATICAL knowledge necessary to carry out all of the above, the methods developed in the subject MATHEMATICS have proven to be the most appropriate for the modern treatment of many disciplines included in the Syllabus. Disciplines that, in the end, will allow the engineer to face the problems that will arise throughout the exercise of the profession.

Therefore, it is necessary to take this subject because it is an essential part of the basic training of a future engineer. Its purpose is to provide students with the basic MATHEMATICAL resources necessary to follow other specific subjects of their degree, so that the student will have enough MATHEMATICAL ability and skills to solve problems related to engineering and to MATHEMATICS itself. In addition, this subject helps to enhance the capacity for abstraction, rigor, analysis and synthesis that are typical of MATHEMATICS and necessary for any other scientific discipline or branch of engineering.

Within the MATHEMATICAL knowledge necessary to carry out all of the above, the methods developed in the field of MATHEMATICS have proven to be the most appropriate for the modern treatment of many disciplines included in the Syllabus. Disciplines that, in the end, will allow the engineer to face the problems that will arise throughout the exercise of the profession.

Therefore, it is necessary to take this subject because it is an essential part of the basic training of a future engineer. Its purpose is to provide students with of the basic MATHEMATICAL resources necessary for the pursuit of other specific subjects of their degree, so that the student will have the ability and MATHEMATICAL have sufficient MATHEMATICAL skills and ability to solve problems related to engineering and to MATHEMATICS itself. In addition, this subject helps to enhance the capacity of abstraction, rigor, analysis and synthesis that are typical of MATHEMATICS and necessary for any other scientific discipline or branch of mathematics. any other scientific discipline or branch of engineering.

4. Degree competences achieved in this course

Course competences
Code	Description
B01	Capacity to solve mathematical problems which might arise in the engineering field. Attitude to apply knowledge about: linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives; numerical methods, numeric algorithms, statistics and optimization.
C01	Capacity to solve ordinary differential equations to be applied in Engineering problems.
C03	To know basic numerical calculus applied to the engineering field.
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.
CB05	Have developed the necessary learning abilities to carry on studying autonomously
CT00	To promote respect and promotion of Human Rights as well as global access principles and design for everybody according to the 10th final order of the Law 51/2003 of December 2nd¿ about equal opportunities, non-discrimination and universal accessibility for people with disabilities.
CT02	To be acquainted with Information and Communication Technology ICT
CT03	Capacity for written and oral communication skills.

5. Objectives or Learning Outcomes

Course learning outcomes
Description
To manage and to know precisely basic concepts of differential geometry
To know the fundamentals and applications of the optimization and to solve and formulate Optimization problems
To know the use of functions of one and several variables including their derivation, integration and graphic representation
To know the main approximations to resolutions by means of numerical methods, to use (at user¿s level) sofware packages of statistics, data processing, mathematical calculations and visualization. to outline algorithms and to program using high level programming language, to visualize functions, geometrical figures and data, to design experiments, analize data and understand results.
Additional outcomes
Description
Know how to describe processes related to mining engineering subjects by means of ordinary differential equations, solve them and interpret the results. To be able to express oneself correctly in oral and written form and, in particular, to know how to use the language of mathematics as a way of expressing with precision the quantities and operations that appear in mining and energy engineering graduat

6. Units / Contents

Unit 1: Elementary concepts. Elementary functions. Limits and continuity.
Unit 2: Differential calculus.
Unit 3: Integral calculus.
Unit 4: Introduction to ordinary differential equations.

ADDITIONAL COMMENTS, REMARKS

Computer classroom practicals:

Practice 1: Introduction to MATLAB. Mathematical functions with MATLAB. Limits and derivatives of functions of one variable.

Practice 2: Approximation of roots of real variable functions.

Practice 3: Integration and 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]	Lectures	B01 C01 C03 CB01 CB02 CB03 CB05 CT02 CT03	1.2	30	N	N	Participative master class, with blackboard and projector.
Problem solving and/or case studies [ON-SITE]	Problem solving and exercises	B01 C01 C03 CB01 CB02 CB03 CB05 CT03	0.7	17.5	Y	N	Participatory resolution of exercises and problems in the classroom. Presentation of academic work consisting of solving exercises and problems individually outside the classroom (progress tests).
Computer room practice [ON-SITE]	Practical or hands-on activities	B01 C01 C03 CB01 CB02 CB03 CB05 CT02	0.4	10	Y	Y	Realisation of problems through the use of computer programmes
Final test [ON-SITE]	Assessment tests	B01 C03 CB01 CB02 CB03 CB05 CT02 CT03	0.1	2.5	Y	Y	The final assessment of the subject includes two partial written tests (not compulsory) and a final written test of the subject that has not been eliminated (compulsory).
Self-study [OFF-SITE]	Self-study	B01 C01 C03 CB01 CB02 CB03 CB05 CT02 CT03	3.6	90	N	N	Autonomous personal study by the student.
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%	The FINAL EXAMINATION will consist of TWO ELIMINATING written INTERIM EXAMINATIONS of subject matter (not compulsory) and a FINAL written EXAMINATION of the subject matter not eliminated (compulsory). These exams will consist of questions, theoretical issues and problems where the approach to the subject or problem, the use of appropriate terminology and 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 will be assessed.
Assessment of activities done in the computer labs	10.00%	10.00%	Evaluation of the practices in the computer classroom, with the application of specific software.
Progress Tests	20.00%	0.00%	To test the progress of the students, at the end of each chapter, they must hand in an academic work consisting of a collection of solved problems in which the problem statement, the use of appropriate terminology and notation to express the ideas and mathematical relations 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 will be assessed.
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:

The FINAL QUALIFICATION for the course will be calculated using the following expression:

0.7*FINAL EXAM + 0.2*PROGRESS TESTS + 0.1*COMPUTER PRACTICALS.

which will be applied provided that the grade of the FINAL TEST is equal to or higher than 4 points. Otherwise, the FINAL QUALIFICATION will be the one obtained in the FINAL TEST.

In order to obtain the mark for the FINAL EXAMINATION, the following procedure will be followed:

1. Students who in the two mid-term exams have obtained a mark equal to or higher than 5 points: the mark in the FINAL EXAM will be the average of the marks obtained in both mid-term exams.

2. Students who in one of the mid-term exams have obtained a mark between 4 and 5 points but whose average with the mark obtained in the other mid-term exam equals or exceeds 5 points: the mark in the FINAL EXAM will be the average of the marks obtained in both mid-term exams.

3. Students, not covered in section 2, who have obtained a grade equal to or higher than 5 points in one of the mid-term exams (eliminating that subject for the final exam) and lower than 5 points in the other mid-term exam: they will have to take the part corresponding to the subject not eliminated in the final exam. The mark in the FINAL EXAM will be the average of the mark obtained in the mid-term exam and the mark obtained in the part of the final exam corresponding to the subject not eliminated.

4. Students who have not passed any of the partial exams: they must take the entire final exam. Their grade in the FINAL EXAM will be the grade obtained in the final exam..
Non-continuous evaluation:

It will be analogous to the continuous assessment, except that the FINAL QUALIFICATION of the subject will be calculated using the following expression:

0.9*FINAL EXAM + 0.1*COMPUTER PRACTICES

Specifications for the resit/retake exam:

There will be a single final written exam where 90% will be questions, theoretical issues and problems where the approach to the topic or problem, the use of appropriate terminology and 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 will be assessed; the remaining 10% will be questions related to the computer practices. The student will decide whether or not to participate in the questions related to the computer practices if he/she wants to improve the grade obtained in them in the ordinary exam.

Specifications for the second resit / retake exam:

There will be a single final written exam where 90% will be questions, theoretical issues and problems where the approach to the topic or problem, the use of appropriate terminology and 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 will be assessed; the remaining 10% will be questions related to the computer practices.

9. Assignments, course calendar and important dates

Not related to the syllabus/contents
Hours	hours
Computer room practice [PRESENCIAL][Practical or hands-on activities]	10
Final test [PRESENCIAL][Assessment tests]	5

Unit 1 (de 4): Elementary concepts. Elementary functions. Limits and continuity.
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	4.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises]	2.25
Self-study [AUTÓNOMA][Self-study]	11

Unit 2 (de 4): Differential calculus.
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	11
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises]	5.25
Self-study [AUTÓNOMA][Self-study]	34

Unit 3 (de 4): Integral calculus.
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	10.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises]	5.25
Self-study [AUTÓNOMA][Self-study]	34

Unit 4 (de 4): Introduction to ordinary differential equations.
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	4
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises]	2.25
Self-study [AUTÓNOMA][Self-study]	11

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	Publishing house	Year	Description	Link
	Calculus.org Resources For The Calculus Student			Algunos recursos en Internet	http://www.calculus.org/
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