Universidad de Jaén

1. Números reales y complejos.
2. Funciones reales de variable real. Cálculo de límites. Estudio de la continuidad.
3. Diferenciacibilidad de funciones reales en una variable. Polinomio de Taylor. Teoremas del valor medio. Problemas de optimización.
4. Métodos generales de integración: Cambio de variable, integración por partes, integración de funciones racionales. Método de Hermite. Integración de funciones trigonométricas. Integración de funciones irracionales.
5. Integral definida. Teorema fundamental del cálculo. Integrales impropias.
6. Matrices. Determinantes. Sistemas de Ecuaciones lineales.
7. Espacio vectorial. Cambio de bases en un espacio vectorial. Producto escalar. Método de ortogonalización de Gram-Schmidt.
8. Diagonalización por semejanza y congruencia de matrices reales.
9. Aplicaciones lineales. Núcleo e imagen de una aplicación lineal. Relación entre las matrices de una aplicación lineal en bases distintas. Formas cuadráticas. Relación entre las matrices de una forma cuadrática en bases distintas
10. Geometría afín. Problemas métricos en el plano y el espacio afín.

• Introducción al Mathematica.
• Conceptos básicos de programación con Mathematica.
• Números complejos.
• Funciones reales. 
• Polinomio de Taylor.
• Método de ortogonalización de Gram-Scmidt.
• Diagonalización por semejanza y congruencia.
• Producto escalar y vectorial.
• Geometría afín.  

Asistencia y/o participación en actividades presenciales y/o virtuales 10 %

Conceptos teóricos de la materia 70 %

Realización de trabajos, casos o ejercicios 20 %

1. Cálculo Infinitesimal De Una Variable . Autor: Burgos, Juan de. Editorial: McGraw-Hill Interamericana.(C. Biblioteca)



2. Cálculo Con Geometría Analítica. Autor: Zill, Dennis G.. Editorial: Grupo Editorial Ieroamérica.(C. Biblioteca)



3. Cálculo Integral: Metodología Y Problemas . Autor: Coquillat, F.. Editorial: Tear Flores.(C. Biblioteca)



4. Mathematica : A Practical Approach . Autor: Blachman, Nancy. Editorial: Prentice Hall.(C. Biblioteca)



5. Calculo I: Teoría Y Problemas De Análisis Matemático En Una Variable. Autor: GLACSA. Editorial: 84-605-0944-3.



6. Variable Compleja Y Aplicaciones. Autor: Churchill, Ruel V.. Editorial: McGraw-Hill.(C. Biblioteca)



7. Curso De Matemáticas Superiores Para Ingenieros. Autor: Mir. Editorial: 5-03-000808-X.



8. Linear Algebra And Geometry . Autor: Shafarevich, Igor R.. Editorial: Springer Berlin Heidelberg.(C. Biblioteca)



9. Calculus . Autor: Grossman, Stanley I.. Editorial: Academic Press.(C. Biblioteca)

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

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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

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