Course guide of Mathematical Methods 3 (2671126)
Departamento de Física Teórica y del Cosmos: 20/06/2022
Departamento de Física Atómica, Molecular y Nuclear: 20/06/2022
Grado (bachelor's degree)
Branch
Module
Subject
Year of study
Semester
ECTS Credits
Course type
Teaching staff
Theory
- Fernando Cornet Sánchez del Águila. Grupo: C
- María Rosario González Férez. Grupo: A
- Roberto Omar Vega Morales. Grupo: B
Practice
- Javier Fuentes Martín Grupos: 2 y 3
- Enrique Ruiz Arriola Grupos: 1 y 2
- Roberto Omar Vega Morales Grupo: 1
Timetable for tutorials
Fernando Cornet Sánchez del Águila
Email- Monday
- 09:00 a 10:00 (Despacho 2)
- 18:00 a 19:00 (Despacho 2)
- Tuesday
- 13:00 a 14:00 (Despacho 2)
- 18:00 a 20:00 (Despacho 2)
- Wednesday de 18:00 a 19:00 (Despacho 2)
María Rosario González Férez
Email- First semester
- Tuesday de 10:00 a 13:00 (Despacho)
- Thursday de 10:00 a 13:00 (Despacho)
- Second semester
- Tuesday de 10:00 a 13:00 (Despacho)
- Thursday de 10:00 a 13:00 (Despacho)
Roberto Omar Vega Morales
Email- Tuesday de 15:00 a 17:00 (Despacho 23)
- Wednesday de 15:00 a 17:00 (Despacho 23)
- Thursday de 15:00 a 17:00 (Despacho 23)
Javier Fuentes Martín
Email- Tuesday de 16:15 a 18:00 (Despacho 21)
- Wednesday de 16:15 a 18:00 (Despacho 21)
- Thursday de 11:30 a 13:00 (Despacho 21)
- Friday de 10:30 a 11:30 (Despacho 21)
Enrique Ruiz Arriola
Email- First semester
- Monday de 11:00 a 13:00 (Despacho)
- Wednesday de 11:00 a 13:00 (")
- Thursday de 11:00 a 13:00 (")
- Second semester
- Monday de 11:00 a 13:00 (")
- Wednesday de 11:00 a 13:00 (")
- Thursday de 11:00 a 13:00 (")
Prerequisites of recommendations
Linear Algebra and Geometry, Calculus, Mathematical Methods I
Brief description of content (According to official validation report)
- Hilbert spaces
- Series expansions, eigenfunctions
General and specific competences
General competences
- CG01. Skills for analysis and synthesis
- CG02. Organisational and planification skills
- CG03. Oral and written communication
- CG05. Skills for dealing with information
- CG06. Problem solving skills
- CG07. Team work
- CG08. Critical thinking
- CG09. Autonomous learning skills
- CG10. Creativity
- CG11. Initiative and entrepreneurship
Specific competences
- CE03. Knowing and understanding the mathematical methods necessary to describe physical phenomena
- CE05. Modelling complex phenomena, translating a physical problem into mathematical language
Objectives (Expressed as expected learning outcomes)
That the student understands the general concepts of Hilbert spaces, especially in their application to Physics, and is able to solve the associated problems.
Detailed syllabus
Theory
Unit 1. Normed spaces and Banach spaces
Unit 2. Euclidean spaces and Hilbert spaces
Unit 3. Function spaces and series
Unit 4. Functions and distributions
Unit 5. Linear operators
Unit 6. Introduction to spectral theory
Bibliography
Basic reading list
1. L. Abellanas y A. Galindo, Espacios de Hilbert, Eudema, 1987.
2. S. K. Berberian, Introducción al espacio de Hilbert, Teide, 1977.
3. P. García González, J. E. Alvarellos Bermejo y J. J. García Sanz, Introducción al formalismo de la mecánica cuántica, U.N.E.D., Madrid, 2001.
4. G. Helmberg, Introduction to spectral theory in Hilbert space, North Holland, 1969.
5. R. P. Kanwall, Generalized functions (theory and technique), Academic Press, 1983.
6. A. N. Kolmogórov y S.V. Fomín, Elementos de la teoría de funciones y del análisis funcional, M.I.R., 1975.
7. R.D. Richtmyer, Principles of Advanced Mathematical Physics, vol. 1, Springer-Verlag, 1978.
8. P. Roman, Some modern mathematics for physicists and other outsiders, vol. 2, Pergamon, 1975.
9. A. Vera López y P. Alegría Ezquerra, Un curso de Análisis Funcional. Teoría y problemas, AVL, 1997.
10. E. Romera Gutiérrez, M. C. Boscá Díaz-Pintado, F. Arias de Saavedra Alías, F. J. Gálvez Cifuentes, J. I. Porras Sánchez, Métodos Matemáticos: Problemas de Espacios de Hilbert, Operadores lineales y Espectros, Paraninfo, 2013.
Recommended links
Teaching methods
- MD01. Theoretical classes
Assessment methods (Instruments, criteria and percentages)
Ordinary assessment session
The evaluation will be carried out mainly from the exams; additionally, the realization of problems and tasks proposed to be solved individually will be considered, by means of which the students will have to demonstrate the acquired knowledge and understanding.
- Passing any of the tests will not be achieved without a thorough and balanced knowledge of all the material.
- In the ordinary call, the final exam grade will constitute 70% of the grade, and the remaining 30% will be evaluated in a complementary way according to: participation in class, delivery of work and/or problems, oral or written assessments
- To pass the course it will be necessary to obtain at least 3 points (out of 10) in the final exam grade.
Extraordinary assessment session
- Final exam with theoretical questions and problems, related to the subject taught in class.
- In extraordinary call, the final exam grade will constitute 100% of the grade.
Single final assessment
- Those students who, following the Regulations of the UGR with terms and deadlines that are required therein, take advantage of this evaluation modality, will carry out the final evaluation only.
- It will consist of a theory and / or exam problems.