Course guide of Mathematical Methods 3 (2671126)

Curso 2022/2023
Approval date:
Departamento de Física Teórica y del Cosmos: 20/06/2022
Departamento de Física Atómica, Molecular y Nuclear: 20/06/2022

Grado (bachelor's degree)

Bachelor'S Degree in Physics




Métodos Matemáticos y Programación


Métodos Matemáticos

Year of study




ECTS Credits


Course type

Compulsory course

Teaching staff


  • Fernando Cornet Sánchez del Águila. Grupo: C
  • María Rosario González Férez. Grupo: A
  • Roberto Omar Vega Morales. Grupo: B


  • Javier Fuentes Martín Grupos: 2 y 3
  • Pablo Sánchez Puertas Grupos: 1 y 2
  • Roberto Omar Vega Morales Grupo: 1

Timetable for tutorials

Fernando Cornet Sánchez del Águila

  • 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

  • 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

  • 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

  • Tuesday de 11:00 a 13:00 (Despacho 21)
  • Wednesday de 14:00 a 16:00 (Despacho 21)
  • Thursday de 14:00 a 16:00 (Despacho 21)

Pablo Sánchez Puertas

  • Tuesday de 15:00 a 17:00 (Despacho)
  • Wednesday de 15:00 a 17:00 (Despacho)
  • Thursday de 15:00 a 17:00 (Despacho)

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


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


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.