1. General information
Course:
CALCULUS II
Code:
56306
Type:
BASIC
ECTS credits:
6
Degree:
419 - UNDERGRADUATE DEGREE PROG. IN MECHANICAL ENGINEERING
Academic year:
2023-24
Center:
106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING
Group(s):
56
Year:
1
Duration:
C2
Main language:
Spanish
Second language:
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
It will be published at the beginning of each semester.
2. Pre-Requisites
In order for students to achieve the learning objectives described, they must have knowledge and skills that are supposed to be guaranteed in their training prior to accessing the University: - Knowledge: basic geometry and trigonometry, basic mathematical operations (powers, logarithms, fractions), polynomials, matrices, derivation, integration and graphic representation of functions. - Basic skills in the handling of instruments: elementary computer management. The programming of Calculus II starts from the assumption that the student has acquired the competences corresponding to the subjects of Calculus I and Algebra. Although there are no formal incompatibilities, students who access a subject without having acquired the competences of the previous subjects, the follow-up of the subject will be much more expensive and difficult both in time and effort.
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 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 technologies in these areas and, where appropriate, generate them, thus responding 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 |
| 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 |
| CEB01 | Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of linear algebra; geometry, differential geometry, differential and partial differential equations, numerical methods, numerical algorithms, statistics and optimisation. |
| CG03 | Knowledge of basic and technological subjects to facilitate learning of new methods and theories, and provide versatility to adapt to new situations. |
| CG04 | Ability to solve problems with initiative, decision-making, creativity, critical reasoning and to communicate and transmit knowledge, skills and abilities in the field of industrial engineering. |
| CT02 | Knowledge and application of information and communication technology. |
| CT03 | Ability to communicate correctly in both spoken and written form. |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Knowledge of the fundamentals and applications of optimisation | |
| Proper management and knowledge of the concepts of differential geometry. | |
| Knowledge of the main approaches for solving by numerical methods, user level implementation of software packages for statistics, data processing, mathematical calculation and visualisation, planning algorithms and programming using a high-level programming language, visualising functions, geometric figures and data, designing experiments, analysing data and interpreting results. | |
| Ability to express oneself correctly orally and in writing and, in particular ability to use the language of mathematics as a way of accurately expressing the quantities and operations that appear in industrial engineering. Acquired habits of working in a team and behaving respectfully. | |
| Management of functions of one and several variables including their derivation, integration and graphic representation. | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Differential calculation on several variables.
-
Unit 2: Differential geometry.
-
Unit 3: Optimization.
-
Unit 4: Multiple integrals.
-
Unit 5: Line and surface integrals.
-
Unit 6: Vectorial analysis.
ADDITIONAL COMMENTS, REMARKS
NOTE.- Taking into account the relationship between its contents, the aforementioned topics can be classified into the following thematic blocks:
BLOCK I.- DIFFERENTIAL CALCULATION OF SEVERAL VARIABLES: Topics 1 and 3
BLOCK II.- INTEGRAL CALCULATION OF SEVERAL VARIABLES: Topics 4, 5 and 6.
BLOCK III.- COMPLEMENTS: Topic 2
Practices in computer classroom:
Practice 1: Introduction and Representation of graphs. Functions, Derivation and Integration of functions with several variables.
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] | Combination of methods | CB02 CB03 CB04 CB05 CT03 | 1.2 | 30 | N | N | Participatory master lesson, with blackboard and projector cannon. | |
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | CB02 CB03 CB04 CB05 CEB01 CG04 CT03 | 0.6 | 15 | Y | N | Solving exercises and problems in the classroom. | |
| Class Attendance (practical) [ON-SITE] | Practical or hands-on activities | CB02 CB03 CB04 CB05 CEB01 CG03 CG04 CT02 CT03 | 0.4 | 10 | Y | Y | Performing problems through the use of computer programs. | |
| Formative Assessment [ON-SITE] | Assessment tests | CB02 CB03 CB04 CB05 CEB01 CG04 CT03 | 0.2 | 5 | Y | Y | Final evaluation of the subject by written test. | |
| Study and Exam Preparation [OFF-SITE] | Self-study | CB02 CB03 CB04 CB05 CEB01 CG03 CG04 CT02 | 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 |
| Progress Tests | 20.00% | 0.00% | To test the progress of the students, they must deliver, at the end of each chapter, an academic work consisting of a collection of solved problems where the approach to the problem will be assessed, 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 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 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. |
| Final test | 70.00% | 90.00% | The FINAL TEST will consist of TWO PRELIMINARY Written PARTIAL EXAMS of matter (Not compulsory) and a written FINAL EXAM of the subject not eliminated in its case (Mandatory). These exams will consist of questions, theoretical questions and problems where the approach to the topic or problem will be evaluated, 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 cleaning and presentation of the document. |
| 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 GRADE of the course will be calculated using the following expression:
0.7*FINAL TEST + 0.2*PROGRESS TESTS +0.1*COMPUTER PRACTICES
which will be applied whenever the qualification of the FINAL TEST is equal to or greater than 4 points. Otherwise, it will be recorded as QUALIFICATION
FINAL the one obtained in the FINAL TEST.
To obtain the qualification of the FINAL TEST, the following procedure will be followed:
1. Students who have obtained a grade equal to or greater than 5 points in the two partial exams: the grade in the FINAL TEST will be the average
of the grades obtained in both partial exams.
2. Students who in one of the partial exams have obtained a grade between 4 and 5 points but for whom the average with the grade
obtained in the other partial exam equals or exceeds 5 points: the grade in the FINAL TEST will be the average of the grades obtained in
both partial exams.
3. Students, not considered in section 2., who have obtained a grade equal to or greater than 5 points in one of the partial exams
(eliminating that subject for the final exam) and less than 5 points in the other partial exam: they must be examined, in the final exam, of the part
corresponding to the matter not eliminated. The grade in the FINAL TEST will be the average between the grade of the approved partial exam and the
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. Your score on the TEST
FINAL will be the one obtained in the final exam. -
Non-continuous evaluation:It will be analogous to the continuous evaluation, except that the FINAL GRADE of the subject will be calculated using the following expression:
0.9*FINAL TEST + 0.1*COMPUTER PRACTICES
Specifications for the resit/retake exam:
A single final written test will be carried out where 90% will correspond to questions, theoretical questions 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 cleaning and presentation of the document; the remaining 10% will be questions related to computing practices. The student will decide whether to participate in
the questions related to the computer science practices if he wants to improve the qualification obtained in them in the ordinary call.
the questions related to the computer science practices if he wants to improve the qualification obtained in them in the ordinary call.
Specifications for the second resit / retake exam:
A single final written test will be carried out where 90% will correspond to 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 the ideas and mathematical relationships used, the choice of procedure most suitable 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% will be questions related to computing practices.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 30 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 15 |
| Class Attendance (practical) [PRESENCIAL][Practical or hands-on activities] | 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 year. The dates of the practices will be specified in the first three school weeks. |
10. Bibliography and Sources