In order for students to achieve the proposed learning objectives, they must possess knowledge and skills that are assumed to be guaranteed in their training prior to university entrance:
- Knowledge: basic geometry and trigonometry, basic mathematical operations (powers, logarithms, fractions), polynomials, matrices, derivation, integration and representation of functions.
- Basic skills in the handling of instruments: elementary handling of computers (operating system).
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.
| 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 |
| CT02 | To be acquainted with Information and Communication Technology ICT |
| CT03 | Capacity for written and oral communication skills. |
| 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 industrial engineering subjects by means of ordinary differential equations and partial derivatives, 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 accurately expressing the quantities and operations that appear in mining and energy engineering. |
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Unit 1: DIFFERENTIAL GEOMETRY.
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Unit 2: FUNCTIONS OF SEVERAL VARIABLES: LIMIT AND CONTINUITY.
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Unit 3: FUNCTIONS OF SEVERAL VARIABLES: DIFFERENTIAL CALCULUS.
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Unit 4: OPTIMIZATION OF SCALAR FUNCTIONS.
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Unit 5: FUNCTIONS OF SEVERAL VARIABLES: MULTIPLE INTEGRALS.
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Unit 6: VECTOR ANALYSIS.
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Unit 7: INTRODUCTION TO DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES.
NOTE: Taking into account the relationship between their contents, the aforementioned subjects can be classified into the following thematic blocks:
BLOCK I.- DIFFERENTIAL CALCULATION OF VARIABLES: Subjects 2, 3 and 4.
BLOCK II.- INTEGRAL CALCULATION OF VARIABLES: Topics 5 and 6.
BLOCK III.- COMPLEMENTS: Topics 1 and 7.
Practical exercises in the computer classroom (MATLAB):
Practice 1: Introduction and Representation of graphs. Functions, Derivation and Integration of functions with several variables.
Practice 2: Optimisation of functions with several variables.
| 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 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 CT03 | 0.4 | 10 | Y | Y | Realization of problems through the use of computer programs. | |
| 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. | |
| Final test [ON-SITE] | Assessment tests | B01 C01 C03 CB01 CB02 CB03 CB05 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). | |
| 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).
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Assessment of activities done in the computer labs | 10.00% | 10.00% | For the evaluation of practices in the computer classroom, with the application of specific software. |
| 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. |
| 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% |
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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 part of 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
.
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2.5 |
| Self-study [AUTÓNOMA][Self-study] | 10 |
| Final test [PRESENCIAL][Assessment tests] | 2.5 |
| Unit 1 (de 7): DIFFERENTIAL GEOMETRY. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 1.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1 |
| Self-study [AUTÓNOMA][Self-study] | 4 |
| Unit 2 (de 7): FUNCTIONS OF SEVERAL VARIABLES: LIMIT AND CONTINUITY. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 3.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Self-study [AUTÓNOMA][Self-study] | 12 |
| Unit 3 (de 7): FUNCTIONS OF SEVERAL VARIABLES: DIFFERENTIAL CALCULUS. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 6.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 4 |
| Self-study [AUTÓNOMA][Self-study] | 24 |
| Unit 4 (de 7): OPTIMIZATION OF SCALAR FUNCTIONS. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1.5 |
| Self-study [AUTÓNOMA][Self-study] | 12 |
| Unit 5 (de 7): FUNCTIONS OF SEVERAL VARIABLES: MULTIPLE INTEGRALS. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 7 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 3.5 |
| Self-study [AUTÓNOMA][Self-study] | 24 |
| Unit 6 (de 7): VECTOR ANALYSIS. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 6 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Self-study [AUTÓNOMA][Self-study] | 10 |
| Unit 7 (de 7): INTRODUCTION TO DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES. | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 1.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1 |
| Self-study [AUTÓNOMA][Self-study] | 4 |
| Global activity | |
|---|---|
| Activities | hours |
| General comments about the planning: | This planning is indicative and may vary depending on the teaching needs of the group of students enrolled. |
