Universidad de Jaén

Menú local

Syllabus 2022-23 - 13511009 - Mathematics 1 (Matemáticas I)

Caption
  • Level 1: Tutorial support sessions, materials and exams in this language
  • Level 2: Tutorial support sessions, materials, exams and seminars in this language
  • Level 3: Tutorial support sessions, materials, exams, seminars and regular lectures in this language
DEGREE: Grado en Ingeniería eléctrica (13511009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Grado en Ingeniería de organización industrial (13011009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Doble Grado en Ingeniería mecánica e Ingeniería electrónica industrial (13911008)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Grado en Ingeniería mecánica (13411009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Doble grado en Ingeniería mecánica e Ingeniería de organización industrial (13811009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Doble grado en Ingeniería eléctrica e Ingeniería electrónica industrial (13711009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Grado en Ingeniería electrónica industrial (13111009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
DEGREE: Doble grado en Ingeniería eléctrica e Ingeniería mecánica (13611009)
FACULTY: SCHOOL OF ENGINEERING OF JAÉN
ACADEMIC YEAR: 2022-23
COURSE: Mathematics 1
SYLLABUS
1. COURSE BASIC INFORMATION
NAME: Mathematics 1
CODE: 13511009 (*) ACADEMIC YEAR: 2022-23
LANGUAGE: English LEVEL: 3
ECTS CREDITS: 6.0 YEAR: 1 SEMESTER: PC
2. LECTURER BASIC INFORMATION
NAME: MOLINA ALBA, FRANCISCA
DEPARTMENT: U124 - MATEMÁTICAS
FIELD OF STUDY: 595 - MATEMÁTICA APLICADA
OFFICE NO.: B3 - 014 E-MAIL: mfmolina@ujaen.es P: 953212033
WEBSITE: -
ORCID: https://orcid.org/0000-0002-4158-0318
LANGUAGE: - LEVEL: 3
NAME: ROSALES RODENAS, Mª CONSUELO
DEPARTMENT: U124 - MATEMÁTICAS
FIELD OF STUDY: 595 - MATEMÁTICA APLICADA
OFFICE NO.: B3 - 005 E-MAIL: mrosales@ujaen.es P: 953212417
WEBSITE: -
ORCID: https://orcid.org/0000-0002-5333-507X
LANGUAGE: - LEVEL: 3
3. CONTENT DESCRIPTION

THEORETICAL CONTENTS.
Topic 1. Introduction to the set of complex numbers.
Real numbers. Properties. Complex numbers. Different ways to express a complex number. Properties.
Operations with complex numbers.
Topic 2. Real functions of real variable. Limit. Continuity.
Real functions of a real variable. Limit of a function at a point. Infinite limits and at infinity.
infinitesimals. Calculation of limits. Indeterminacies in the calculation of limits. Continuous function at a point.
Properties. Discontinuities. Theorems.
Topic 3. Derivation.
Derivative of a function at a point. Application of the derivative concept. Algebra of derivatives. Implicit derivative.
Logarithmic derivative. Derivative of a composite function. Derivative of an inverse function.
Higher order derivatives. Theorems. L'Hôpital rule. Shape properties of a function. Extremes. Optimization.
Topic 4. Integration.
indefinite integral. Definite integral. Properties. General integration methods. fundamental theorem of the
Calculus. Barrow's rule. Geometric applications of the definite integral.
Topic 5. Matrices. Determinants.
Arrays. Operations with matrices. Determinants. Properties of determinants. Rank of an array.
Topic 6. Systems of linear equations.
Definitions. Types of systems of linear equations. Rouche-Frobenius theorem. Methods of
resolution. Systems of homogeneous linear equations.
Topic 7. Vector spaces.
Vector spaces. Vector subspaces. Characterization and properties. linear dependence and linear independence.
Basis and dimension of a vector space.
Topic 8. Diagonalization of a square matrix.
Eigenvalues and eigenvectors of a square matrix. Characteristic polynomial and characteristic equation.
Diagonalization of a square matrix. Applications.
Topic 9. Geometry.
Coordinates and vectors in space. Cross product of two vectors. Lines and planes in space.
conics and quadrics.
PRACTICAL CONTENTS
Problems and practical issues related to the same contents that have been explained in the 9 topics of theoretical
content. Mathematica software will be used for the study and resolution of such problems and practical issues.
1. Introduction to the Mathematica program. Solving complex number problems.
2. Practices on real functions of real variables, graphs, limits and continuity.
3. Practices on derivation and the applications of the derivative.
4. Practices on integrals and applications.
5. Practices on matrix calculation.
6. Practices on systems of linear equations.
7. Practices on vector spaces
8. Practice on values and eigenvectors of a matrix.
9. Practice on Geometry.

4. COURSE DESCRIPTION AND TEACHING METHODOLOGY

DETAILED INFORMATION:
Topics will be developed in theory class, emphasizing logical reasoning and inference. It will be promoted the
correct use of mathematical language, its understanding and application (Result 8).
Mathematical concepts will be applied in appropriate examples (Result 2). Exercises to be solved will propose
practical cases for the students to study and solve by analyzing, investigating and applying the necessary
procedures and reasoning (CBB1R Competency, Result 1, Result 3 and Result 5).
The students will have audiovisual material that they must work with before the theory classes, according to
instruction of the teacher. In this way, the autonomous work of the students is encouraged (Result 4) and,
reinforces CB1R competence.
Practices will be carried out using mathematical software in computer rooms, proposing to students the
resolution of exercises with the computer (Result 8, Result 5).

The final grade of the course for the student who does not take the theory exam will be the no-show.

 

The active participation in the practice class will be evaluated from the proposed exercises that must be done in the computer room.

 

The grades obtained in the practice class in the evaluation of section S1 will be kept in all the examinations during the same academic year in which they were taken.

 

The core competencies and learning outcomes will be assessed using the following instruments: Attendance and/or participation in face-to-face and/or virtual activities, theoretical concepts of the subject, Performance of works, cases or exercises and laboratory/field/use of ICT tools.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

5. ASSESSMENT METHODOLOGY

The rating system is governed by the provisions of RD 1125/2003 of September 5, which establishes the
European system of credits and the system of qualifications in university degrees of official character
DETAILED INFORMATION:
To pass the subject it will be necessary to achieve a grade of five points out of ten. This rating will be obtained
as a weighted average of the blocks S1 (active participation in practical classes), S2 (theoretical concepts of the
subject) and S3 (completion of works, cases and exercises). To make this average It will be essential to have
obtained a minimum of 5 out of 10 points in the theoretical part (Block S2).
A final exam will be held on the date determined by the center. This exam will evaluate the acquisition of the
CB1R and CBB1R Competencies and achievement of Results 1, 2, 3 and 8. The final grade for the subject for
students who do not take the theory exam will not be shown.
Active participation in class practices (S1) will be evaluated with the completion of two proposed exercises:
first on contents of Calculus and, second on contents of Linear Algebra and Geometry (assessment of
Results 4 and 5).
At the end of the semester, in practice class, an exam will be carried out using the Mathematica program in the
resolution of the proposed problems (S3).
The grades obtained in the practical class in the evaluation of section S1 (active participation in practice class)
and S3 (practice exam), will be kept in all exam calls for the same academic year in which they were made.

6. BOOKLIST
MAIN BOOKLIST:
  • Exercises in linear algebra Luis Barreira, Claudia Valls. Edition: -. Author: Barreira, Luís.. Publisher: World scientific  (Library)
8. VIRTUAL / CLASSROOM TEACHING SCENARIO

Presentiality:

According to different parameters (number of students enrolled per group, assigned classroom capacity and distance between students), the minimum number of subgroups in which each theory or practice group must be subdivided will be determined to ensure that attendance is carried out with the health guarantees established by the competent authority.

Classroom teaching in the multimodal or mixed scenario will be: non-rotational when possible for 100% of the students, and rotational when not possible.

The percentage of attendance, taking into account the parameters mentioned above, will be established and specified by the Centre. In general, and as these are estimates, we will take as a reference the one provided in July 2020 by the Centre: 50% for each of the theory groups (2 subgroups) and 50% for each of the practice groups (2 subgroups). These percentages will be set by the Centre before the start of the classes. If the percentage estimates were to improve due to any circumstance (reduction of the minimum distance between people, use of adjacent teaching spaces, etc.) and allowed higher percentages of attendance, these would always be chosen, and the least number of subgroups possible would be taken, with 100% attendance being understood as the most optimum case.

Timing:

The timing and schedule will be the same in any scenario: if attendance is 100%, a rotating system or an exclusively online teaching system. The only thing that will vary is the teaching methodology.

Methodology:

- If a system of weekly rotation of face-to-face teaching is established, each subgroup will receive face-to-face teaching for a full week, alternating with the other subgroups. The sub-group of students will be attended by the teacher that week, while the rest of the students attend the class, (according to the instructions given by the Centre), by means of video-conference retransmission (1).

- Expository classes in big groups, presential/online (1) rotating 50% (or a different percentage according to the indications of the Center), where a great part of the contents of the subject will be exposed, as well as type examples will be shown.

- Classes in practice groups, face-to-face/online (1) 50% (or a different percentage according to the indications of the Centre), in which problems related to the contents exposed in the classes in large groups will be solved with the help of the computer. At the same time, in these classes the theoretical contents of the subject that are not exposed in the exposition classes will be exposed in a more practical way. Finally, they will be solved on the blackboard, and whenever possible using the computer, standard exercises of the subject that have been previously proposed to the student to work on at home.

Evaluation:

To pass the course, in any scenario, it is necessary to obtain a grade of 5 out of 10 points. This grade will be obtained as a weighted average of blocks S1, S2 and S3. To achieve this average, it is also essential to have obtained a minimum of 4 out of 10 points in the theoretical part. If the minimum is not reached, the grade reflected in the minutes will be a maximum of 4 out of 10.

The block "Mastery of the theoretical contents of the subject and problem solving" (S2) will be evaluated by a final exam with 60% of the total weight of the subject

The "Completing assignments, cases, or exercises" block (S3) has a 20% weight in the course evaluation and will consist of two practice tests with Mathematica. The first (50%) will be related to problem solving in topics 1-4 and the second (50%) in topics 5-8

The block "Active participation in practice classes" (S1) has a weight of 20% in the evaluation of the subject and will consist of the completion of exercises or questionnaires from each block.

In the extraordinary calls, all the blocks will be evaluated in the same way as in the ordinary ones, or, if the student requests it, with a final exam with a weight of 100% to guarantee the fulfillment of the current rule.

Grades in blocks S2 and S3, which exceed 5 out of 10 points, if the subject has not been passed, will be maintained in each of the official calls for the academic year.

The blocks, percentages and evaluation will be the same in the mixed and classroom scenarios, varying exclusively the evaluation methodology, and in particular the exercises or exams, which will be either classroom or online. Whenever possible, the exercises or exams will be done in person.

In the classroom examinations of each call or in any scoring exercise in class that is made, except in special and particular circumstances that will be specified by your teacher, no electronic devices, notes, books or any other medium that allows the storage or transmission of data will be allowed. In the event of non-compliance, action will be taken in accordance with the regulations in force.

The exams will be held, preferably, in person. They will only be held online in accordance with the recommendations provided by the University of Jaén.

An online and oral evaluation will be used for those students who have technical or other difficulties (duly justified) that occur during the evaluation process, or when the teaching staff cannot verify the authorship of the tests taken.

The instructions, which must be complied with, for online exams and exercises, continuous assessment or official announcements, will be published sufficiently in advance in virtual teaching. These will include the compatibility of taking all the online tests with the use of webcams, recordings, etc. according to the guidelines given by the university.

Each exercise of the exam must be carried out with the techniques and procedures taught in class. Likewise, they must be argued, reasoned, explained and accompanied by the necessary intermediate operations until the final result is reached.

Each student must have the necessary technical means to be able to take the exams online, such as a computer, webcam, microphone and the software required in each case. In this sense, according to instructions received from the General Secretariat of the University of Jaén, the teaching staff must comply with the duty of information set out in Article 13 of the General Regulations on Data Protection (Regulation (EU) 2016/679 of the European Parliament and Council of 27 April 2016) and inform of the recording of the exam by video call, through Google's Hangouts Meet platform (2), as an essential instrument for guaranteeing the transparency of the process.

9. VIRTUAL TEACHING SCENARIO

Presentiality:

Teaching will be exclusively online.

Timing:

The timing and schedule will be the same in any scenario: if attendance is 100%, a rotating system or a teaching system exclusively online. The only thing that will vary is the teaching methodology.

Methodology:

- Expository classes in large groups online (1), where a large part of the contents of the subject will be exposed, as well as type examples will be shown.

- Classes in groups of online practices (1), in which problems related to the contents exposed in the classes in large groups will be solved with the help of the computer. At the same time, the theoretical contents of the subject that are not presented in the lectures will be presented in a more practical way. Finally, they will be solved on the blackboard, and whenever possible using the computer, standard exercises of the subject that have been previously proposed to the student to work on at home.

Evaluation:

To pass the subject, in any scenario, it is necessary to obtain a grade of 5 out of 10 points. This grade will be obtained as a weighted average of blocks S1, S2 and S3.  To achieve this average, it is also essential to have obtained a minimum of 4 out of 10 points in the theoretical part (Block S2). If the minimum is not reached, the grade reflected in the minutes will be a maximum of 4 out of 10.

The block "Mastery of the theoretical contents of the subject and problem solving" (S2) will be evaluated by a final exam with 60% of the total weight of the subject

The "Completing assignments, cases, or exercises" block (S3) has a 20% weight in the course evaluation and will consist of two practice tests with Mathematica. The first (50%) will be related to problem solving in topics 1-4 and the second (50%) in topics 5-8

The block "Active participation in practice classes" (S1) has a weight of 20% in the evaluation of the subject and will consist of the completion of exercises or questionnaires from each block.

In the extraordinary calls, all the blocks will be evaluated in the same way as in the ordinary ones, or, if the student requests it, with a final exam with a weight of 100% to guarantee the fulfillment of the current rule.

Grades in blocks S2 and S3, which exceed 5 out of 10 points, if the subject has not been passed, will be maintained in each of the official calls for the academic year.

The blocks, percentages and evaluation will be the same in the mixed and classroom scenarios, varying exclusively the evaluation methodology, and in particular the exercises or exams, which will be either classroom or online. Whenever possible, the exercises or exams will be done in person.

In the classroom examinations of each call or in any scoring exercise in class that is made, except in special and particular circumstances that will be specified by your teacher, no electronic devices, notes, books or any other medium that allows the storage or transmission of data will be allowed. In the event of non-compliance, action will be taken in accordance with the regulations in force.

The exams will be held, preferably, in person. They will only be held online in accordance with the recommendations provided by the University of Jaén.

An online and oral evaluation will be used for those students who have technical or other difficulties (duly justified) that occur during the evaluation process, or when the teaching staff cannot verify the authorship of the tests taken.

The instructions, which must be complied with, for online exams and exercises, continuous assessment or official announcements, will be published sufficiently in advance in virtual teaching. These will include the compatibility of taking all the online tests with the use of webcams, recordings, etc. according to the guidelines given by the university.

Each exercise of the exam must be carried out with the techniques and procedures taught in class. Likewise, they must be argued, reasoned, explained and accompanied by the necessary intermediate operations until the final result is reached.

Each student must have the necessary technical means to be able to take the exams online, such as a computer, webcam, microphone and the software required in each case. In this sense, according to instructions received from the General Secretariat of the University of Jaén, the teaching staff must comply with the duty of information set out in Article 13 of the General Regulation on Data Protection (Regulation (EU) 2016/679 of the European Parliament and Council of 27 April 2016) and report the recording of the exam by video call, through the Google Hangouts Meet platform(2), as an essential instrument for guaranteeing the transparency of the process.

DATA PROTECTION CLAUSE (on line exams)

Institution in charge of data processing: Universidad de Jaén, Campus Las Lagunillas, s/n, 23071 Jaén

Data Protection Delegate: dpo@ujaen.es

Purpose: In accordance with the Universities Law and other national and regional regulations in force, carrying out exams and assessment tests corresponding to the courses students are registered in. In order to avoid frauds while sitting the exam, the exam will be answered using a videoconference system, being able the academic staff of the University of Jaén to compare and contrast the image of the person who is answering the exam with the student's photographic files. Likewise, in order to provide the exam with evidential content for revisions or claims, in accordance with current regulation frameworks, the exam will be recorded and stored.

Legitimacy: compliance with legal obligations (Universities Law) and other national and regional regulations currently in force.

Addressees: service providers who are the owners of the platforms where the exams are carried out and with whom the University of Jaén has signed the corresponding data access contracts.

Storage periods: those established in current in force regulations. In the specific case of exam videoconference recordings, not before the examination records and transcripts are closed or the exam can still be reviewed or challenged.

Rights: you can exercise your right of access, amendment, cancellation, opposition, suppression, limitation and portability by sending a letter to the postal or electronic address indicated above. In the event that you consider that your rights have been violated, you may submit a complaint to the Andalusian Council for Transparency and Data Protection www.ctpdandalucia.es

CLASS RECORDING CLAUSE PERSONAL DATA PROTECTION

Person in charge: Universidad de Jaén, Paraje Las Lagunillas, s/n; Tel.953 212121; www.ujaen.es

Data protection delegate (DPO): TELEFÓNICA, S.A.U. ; Email: dpo@ujaen.es

Procedure aim: To manage proper recordings of teaching sessions with the aim of facilitating learning process under a multimodal and/or online teaching

Period for record storage: Images will be kept during legal term according to regulations in force

Legitimacy: Data will be managed according to legal regulations (Organic Law 6/2001, December 21, on Universities) and given consent provided by selecting corresponding box in legal admission documents

Data recipients (transfers or assignments): Any person allowed to get access to every teaching modality

Rights: You may exercise your rights of access, rectification, cancellation, portability, limitation of processing, deletion or, where appropriate, opposition. To exercise these rights, you must submit a written request to the Information, Registration and Electronic Administration Service of the University of Jaen at the address above, or by e-mail to the address above. You must specify which of these rights you are requesting to be satisfied and, at the same time, you must attach a photocopy of your ID card or equivalent identification document. In case you act through a representative, legal or voluntary, you must also provide a document that proves this representation and identification. Likewise, if you consider that your right to personal data protection has been violated, you may file a complaint with the Andalusian Data Protection and Transparency Council www.ctpdandalucia.es