Course guide of Mathematical Methods 3 (2671126)

Curso 2023/2024
Approval date:
Departamento de Física Teórica y del Cosmos: 22/06/2023
Departamento de Física Atómica, Molecular y Nuclear: 23/06/2023

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


  • Javier Fuentes Martín. Grupo: B
  • María Elvira Gámiz Sánchez. Grupo: A
  • Eugenio Megías Fernández. Grupo: C


  • María Elvira Gámiz Sánchez Grupo: 2
  • José Ignacio Illana Calero Grupo: 1
  • Eugenio Megías Fernández Grupos: 1 y 2
  • Roberto Omar Vega Morales Grupo: 3

Timetable for tutorials

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)

María Elvira Gámiz Sánchez

  • Monday de 10:00 a 12:00 (Despacho A3 Mod-A)
  • Tuesday de 10:00 a 12:00 (Despacho A3 Mod-A)
  • Wednesday de 15:00 a 17:00 (Despacho A3 Mod-A)

Eugenio Megías Fernández

  • First semester
    • Monday
      • 10:00 a 12:00 (Despacho)
      • 17:00 a 18:00 (Despacho)
    • Tuesday de 17:00 a 18:00 (Despacho)
    • Wednesday de 10:00 a 11:00 (Despacho)
    • Thursday de 10:00 a 11:00 (Despacho)
  • Second semester
    • Monday de 10:00 a 12:00 (Despacho)
    • Wednesday de 10:00 a 12:00 (Despacho)
    • Thursday de 10:00 a 12:00 (Despacho)

José Ignacio Illana Calero

  • Monday de 11:00 a 13:00 (Despacho 4)
  • Wednesday de 11:00 a 13:00 (Despacho 4)
  • Friday de 11:00 a 13:00 (Despacho 4)

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)

Prerequisites of recommendations

Linear Algebra and Geometry I and II, Calculus I, and 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 expansions.
Unit 4. Functionals 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. Additional consideration will be given to the individual solution of problems and/or tasks, from which the students will demonstrate the acquired knowledge and understanding.

  • In the ordinary call, the final exam grade will constitute 70% of the grade (A), and the remaining 30% (B) will be evaluated in a complementary way according to one or more of the following criteria: participation in class, submission of problems and/or tasks, oral or written assessments,...
  • To pass the course it will be necessary to obtain at least 4 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.
  • As a general rule, the exam will correspond to 100% of the grade. However, upon student request, the exam will count towards 70% of the grade, with the remaining 30% corresponding to the grade obtained in part B of the ordinary call. In this case, it will be necessary to obtain at least 4 points (out of 10) in the final exam 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 an exam involving theoretical questions and/or problems.