Universidad de Jaén

Chapter 1: Functions. The real line. Real functions of one variable. Main functions in Analysis and Economy. Limits and continuity. Economic modelling by means of functions and limits.

Chapter 2. Differentiation of functions. The derivative, pointwise rate of change in economic modelling, geometric interpretation. Computations of derivatives. Derivative and shape preserving properties of a function. L'Hôpitâl theorem.

Chapter 3. Integration of functions. Primitive of a function, indefinite integral and its properties. Computation of primitives. Definite integral and its properties. Applications of the definite integral.

Chapter 4. Matrices. Data representation by means of matrices. Basic definitions and matrix operations. Matrix power and matrix iterative models. Rank of a matrix. Determinant. Inverse matrix.

Chapter 5. Systems of linear equations. Vectors. Classification of systems of linear equations. Parametric expression of the solution of a linear system. Cramer's Rule and Gauss Elimination. Linear subspace. Basis, coordinates and dimensión for linear subspaces.

Chapter 6. Matrix diagonalization. Diagonalization process: eigenvalues, eigenvectors and characteristic polynomial. Interpretation of eigenvalues and eigenvectors and tendence in iterative matrix models. Tendency study in matrix models.

Classes of theory for all the group (big group): The theoretical aspects of the subjects will be exposed along with general practical examples.

Problems classes in small groups: 15 hours will be devoted to the resolution of problems and exercises with applications in Economy.

Computer classes in small groups: 15 hours will be carried out in the computer laboratory with the aid of the software Wolfram Research 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.

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.

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

Items considered to compute the mark:

(S1)   (1 point = 10% of the total mark) Attendance and/or participation: The attendance to the theory, problems and computer classes will be considered taking into account the active participation of the students, in the terms that the professor will determine.  

(S2)   (8 points = 80% of the total mark) Basic theorical and practical concepts of the subject.

1. Theory/problems, 6 points (70%): Written exam at the end of the quarter . Alternatively, a continuous assesment system could be proposed to obtain this 7 points along the quarter.
2. Computer practices, 2 point (10%): Exam in the computer classroom at the end of the quarter . Alternatively, a continuous assesment system could be proposed to obtain the point of this item along the quarter.

(S3)   (1 point = 10% of the total mark) Works, exercises or short exams proposed by the professor along the quarter.

Unless a continuous assesment system which indicates the contrary is proposed, the following criteria will also be applied:

*The points obtained in (S1) and (S3) will be maintained for all the official exam calls of the course.

*The mark obtained in the exam of computer practices, item (S2)-2, will be maintained for all the official exam calls of the course. Only the last mark obtained in an official practices exam will be considered no matter if the student had better marks in previous calls.

*The final mark of those students that did not attend the theory exam, item (S2)-1, will be 'No Presentado' no matter if they participate in any of the rest of the activities of the course.

*The final mark will be sum of the points obtained in (S1), (S2) and (S3) provided that in item (S2)-1 the student obtains at least 3 points (out of 10).

1) TEACHING METHODOLOGY AND ACTIVITIES

2)    Assesment system  

The assesment system with all aspects and weights will be the one indicated for the face-to-face scenary.

The assesment for Attendance/participation  (S1) and Works/exercises/short exams (S3) will be based on the on-line tools that are also used for the face-to-face modality.

The exams in item (S2) will be hold face-to-face preferably. In case that this is impossible due to number of classrooms and technical means available, an on-line videoconference exam system will be used.

3) RESOURCES

For the on-line teaching computer, tablet or mobile phone with internet connection and Wolfram Research Mathematica software installed is required. A document scanning application will be also necessary. Besides, we will make use of the Docencia Virtual system of the University of Jaén, the platform SiDoc of the Department of Mathematics as well as the Google tools offered by the University of Jaén. Moreover, the bibliographic electronic resources abailable through the Library of the University of Jaen will be employed.

1) TEACHING METHODOLOGY AND ACTIVITIES

2) ASSESMENT SYSTEM

The assesment system with all aspects and weights will be the one indicated for the face-to-face scenary.

The assesment for Attendance/participation  (S1) and Works/exercises/short exams (S3) will be based on the on-line tools that are also used for the face-to-face modality.

The exams in item (S2) will be on-line by videoconference.

3) RESOURCES

For the on-line teaching computer, tablet or mobile phone with internet connection and Wolfram Research Mathematica software installed is required. A document scanning application will be also necessary. Besides, we will make use of the Docencia Virtual system of the University of Jaén, the platform SiDoc of the Department of Mathematics as well as the Google tools offered by the University of Jaén. Moreover, the bibliographic electronic resources abailable through the Library of the University of Jaen will be employed.

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

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