## Syllabus 2022-23 - 11811013 - 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: Doble grado en Derecho y Administración y dirección de empresas FACULTY: FACULTY OF LAW AND SOCIAL SCIENCES ACADEMIC YEAR: 2022-23 COURSE: Mathematics 1
SYLLABUS
1. COURSE BASIC INFORMATION
 NAME: Mathematics 1 CODE: 11811013 ACADEMIC YEAR: 2022-23 LANGUAGE: English LEVEL: 3 ECTS CREDITS: 6.0 YEAR: 1 SEMESTER: SC
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: GUERRERO GARCIA, JULIO DEPARTMENT: U124 - MATEMÁTICAS FIELD OF STUDY: 595 - MATEMÁTICA APLICADA OFFICE NO.: B3 - B3-035 E-MAIL: jguerrer@ujaen.es P: 953 213375 WEBSITE: - ORCID: - LANGUAGE: - LEVEL: 3
3. CONTENT DESCRIPTION

Unit 1. Functions. The real line.

Real-valued functions of one real variable. Elementary functions. Limits and continuity of real-valued functions of one real variable. Modelization of economic phenomena using functions and the concept of limit.

Unit 2. Differentiability of real-valued functions of one real variable.

The concept of derivative, velocity or instantaneous rate change in phenomena modelized by functions. Geometrical interpretation of derivative. Differentiation rules. Relative extremes, convexity, concavity and inflection points. L'Hôpital Theorem.

Unit 3. Integration of functions.

Primitive, Indefinite integral and properties. Integration rules. Definite integral and properties. Aplications of the definite integral.

Unit 4. Matrices.

Data representation using matrices. Basic definitions and matrix operations. Matrix powers and iterative matrix models. Matrix rank. Determinants. Inverse matrix.

Unit 5. Linear systems of equations.

Vectors. Classification of  linear systems of equations. Parametric solution of a linear system. Gauss and Cramer methods to solve linear systems of equations. Vector subspaces. Bases, coordinates and dimension of vector subspaces.

Unit 6. Diagonalization of matrices.

Eigenvalues and eigenvectors, characteristic polynomial. Interpretation of eigenvectors and eigenvalues in matrix iterative processes. Role of dominant eigenvector and eigenvalue in asymptotic behaviour of matrix iterative processes.

Practical Content:

Home assignments and computer practises related with the content of the course.

4. COURSE DESCRIPTION AND TEACHING METHODOLOGY

Lectures (M1, M3, M4, M5): Theoretical contents and related practical examples will be developed in these sessions.

Seminars (M6, M7, M8, M10, M12, M13): 15 one-hour long classroom sessions will be devoted for solving problems, with special emphasis on applications to economics. Additionally, 15 one-hour long computer lab sessions will be devoted for solving problems by using the software Mathematica.

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

1. Detail:

S1. ACTIVE ATTENDANCE: 0 points (0%):

S2. THEORETICAL CONCEPTS: 7.0 points (70%): Final written exam about the theoretical concepts and related exercises.

S3. CLASSROOM EXERCISES AND PROJECTS: 1.0 point (10%):

Realization of individual and/or group projects with oral presentation to the rest of the class. Realization of classrom exercises proposed by the profesor.

S4. COMPUTER LAB PRACTICES: 2.0 points (20%): Computer exam. Computer guidelines may be used in the exam. Learning results R11 and R13.

The final grade will be the sum of the marks obtained from S2, S3, S4.
This will be possible only when S2 has been passed. Otherwise, the final
grade will be the mark obtained from S2 only.

For the English group the evaluation of S2 and S4 will be achieved
during the course without the need of final exams. However, they will
appear as 'SHOWN' in the grade list for the corresponding official exam
call irrespectively of the fact that they attend or not the final exams.

Marks from S3 and S4 will be maintained during the current academic
year. In the Ordinary Session II or the Special Session II students can
take the exam of S2 but in this case the grade will be last one obtained.

The skills and learning results obtained in each evaluation aspect are related in the following way:

Skill CE7ADE: Aspects (S2) (S3) (S4)
Skill G3ADE: Aspects (S2) (S3) (S4)
Learning Result R11: Aspects (S2) (S3) (S4)
Learning Result R12: Aspect (S3)
Learning Result R13: Aspect (S4)
Learning Result R14: Aspects (S2) (S3) (S4)

6. BOOKLIST
MAIN BOOKLIST:
• Essential mathematics for economic analysis. Edition: 5th ed. Author: Sydsaeter, Knut. Publisher: Harlow : Pearson Education Limited, 2016  (Library)
• Calculus. Edition: 12th . Author: Larson, R. & Edwards, B.H.. Publisher: Cengage Learning.
• Notes: English Edition
(Library)
7. VIRTUAL / CLASSROOM TEACHING SCENARIO

TEACHING METHODOLOGIES AND FORMATIVE ACTIVITIES

 Formative Activities  (1) Format (in person/Off-site) (2) Teaching Methodology  Description 30 theoretical sessions with the course content Classrom based 25% -  50% 30 one-hour lectures, realized in the classroom and video streamed by videoconference to the rest of the group. Periodic rotation of in-person students. 15 computer lab sessions Clasroom based 25% - 50% 15 one-hour practical sessions in computer lab, with periodic rotation of in-person students.  Streamed by videoconference to the rest of the group. 15 tutorial sessions Clasroom based  25% al 50% 15 one-hour tutorials (reduced groups, rotation of in-person students and streamed by videoconference to the rest of the group). Office hours Off-site Office hours will be online using videoconference or email.

( 1 ) In the off-site scenerio,  course lecturers reserve the right to refuse the recording, transmission or reproduction of its image, voice and speech during their lectures at Universidad de Jaén.

(2) The Faculty is responsible for fixing the ratio of in-person and off-site students when the final number of them and the assigned lecture room are known.

EVALUATION SYSTEM

 Evaluation test Format (in-person/off-site sincronous o asincronous) Description Percentage (S2) Final written exam. In person Final written exam with theoretical and  practical content. 60 % (S3) Realization of a project with applications of the theoretical contents. Realization of  assigned exercises Off-site Structure of the project. Quality of the document. Exposition to the professor and/or classroom. Submission of the exercises correctly solved 10 % (S4.1) Computer lab exercises with Mathematica. In-person/ Off-site Two computer based tests during the course. 10% (S4.2) Computer lab exercises with Mathematica. In person Final exam at the end of the semester 20%

RESOURCES

• Basic and complementary  bibliography contain electronic bibliographic resources at disposal in the university library.
• Resources needed  for off-site  follow-up of masterclass lectures, tutorials, realization of classrom exercises, ... (Google Meet, Google Form, YouTube, Docencia Virtual, ...)
• Tablets and/or 2-in-1 laptops, substituting the blackboard, to use during videoconferences.
•  Self-evaluation tests designed by the course lecturers.
• Software of own design for the random generation of unique exams from a large database of questions.
• Students should install at home the software Mathematica for the off-site realization of computer exercises.
• Students should fulfill the technical requirements for the correct realization of distance exams. This includes: laptop, webcam, microphone and the required software. Course lecturers will inform of the video and audio recording of the videconference exams using Google Meet, to guarantee the transparency of the process.

8. VIRTUAL TEACHING SCENARIO

TEACHING METHODOLOGIES AND FORMATIVE ACTIVITIES

 Formative Activities  (1) Format (in person/Off-site) Teaching Methodology  Description 30 theoretical sessions with the course content Off-site 30 one-hour lectures streamed by videoconference. 15 computer lab sessions Off-site 15 one-hour practical sessions by videoconference. 15 tutorial sessions Off-site 15 one-hour tutorials by videoconference. Office hours Off-site Office hours will be online using videoconference or email.

( 1 ) In the off-site scenerio, course lecturers reserve the right to refuse the recording, transmission or reproduction of its image, voice and speech during their lectures at Universidad de Jaén.

EVALUATION SYSTEM

 Evaluation test Format (in-person/off-site sincronous o asincronous) Description Percentage (S2) Final written exam. Off-site Final written exam with theoretical and  practical content. 60 % (S3) Realization of a project with applications of the theoretical contents. Realization of  assigned exercises Off-site Structure of the project. Quality of the document. Exposition to the professor and/or classroom. Submission of the exercises correctly solved 10 % (S4.1) Computer lab exercises with Mathematica. In-person/ Off-site Two computer based tests during the course. 10% (S4.2) Computer lab exercises with Mathematica. Off-site Final exam at the end of the semester 20%

RESOURCES

• Basic and complementary  bibliography contain electronic bibliographic resources at disposal in the university library.
• Resources needed  for off-site  follow-up of masterclass lectures, tutorials, realization of classrom exercises, ... (Google Meet, Google Form, YouTube, Docencia Virtual, ...)
• Tablets and/or 2-in-1 laptops, substituting the blackboard, to use during videoconferences.
•  Self-evaluation tests designed by the course lecturers.
• Software of own design for the random generation of unique exams from a large database of questions.
• Students should install at home the software Mathematica for the off-site realization of computer exercises.
• Students should fulfill the technical requirements for the correct realization of distance exams. This includes: laptop, webcam, microphone and the required software. Course lecturers will inform of the video and audio recording of the videconference exams using Google Meet, to guarantee 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