Course guide of Mathematical Methods 3 (2671126)

• Linear Algebra and Geometry I and II, Calculus I, and Mathematical Methods I
• When utilizing AI tools for this course, students are expected to adopt an ethical and responsible approach. The recommendations outlined in the "Recommendations for the Use of Artificial Intelligence at the UGR" document, available at this link: https://ceprud.ugr.es/formacion-tic/inteligencia-artificial/recomendaciones-ia#contenido0, must be followed.

• 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 expansions.
Unit 4. Linear operators and introduction to spectral theory.
Unit 5. Functionals and distributions.

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. 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 the following criteria: submission of problems and tasks, and/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.

• 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.

• In accordance with the UGR's Regulations on Student Assessment and Grading, a single final assessment is available for students who are unable to participate in the continuous assessment method due to any of the reasons stipulated in Article 8. To opt for this single final assessment, students must submit a request via the electronic portal within the first two weeks of the course's instruction, or within two weeks following their enrollment if it occurs later. Exceptions may be made for overriding unforeseen circumstances that arise after these initial periods. The request must clearly state and provide evidence for the reasons preventing their participation in the continuous assessment system. the exam will correspond to 100% of the grade.
• It will consist of an exam involving theoretical questions and/or problems.

Students with Specific Educational Support Needs (SESN) Following the recommendations from the CRUE and the UGR's Secretariat for Inclusion and Diversity, the systems for acquiring and assessing competencies outlined in this teaching guide will be applied in accordance with the principle of universal design. This approach aims to facilitate learning and the demonstration of knowledge, aligning with the needs and functional diversity of the student body. Teaching methodology and assessment will be adapted for students with SESN, in line with Article 11 of the UGR's Regulations on Student Assessment and Grading, published in the Official Bulletin of the UGR No. 112, dated November 9, 2016. UGR Inclusion and Diversity For students with disabilities or other SESN, the tutoring system must be adapted to their needs, in accordance with the UGR's Inclusion Unit recommendations. Departments and Centers must establish appropriate measures to ensure that tutoring sessions are held in accessible locations. Furthermore, faculty may request support from the University's competent unit when special methodological adaptations are required.

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).