Course guide of Mathematical Methods 3 (2671126)

Linear Algebra and Geometry, Calculus, Mathematical Methods I

• Hilbert spaces
• Series expansions, eigenfunctions

That the student understands the general concepts of Hilbert spaces, especially in their application to Physics, and is able to solve the associated problems.

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

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.

• MD01. Theoretical classes

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.

• 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.

• 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.