Subject
Mathematical Tools
General details of the subject
- Mode
- Face-to-face degree course
- Language
- English
Teaching staff
| Name | Institution | Category | Doctor | Teaching profile | Area | |
|---|---|---|---|---|---|---|
| BRIZUELA CIEZA, DAVID | University of the Basque Country | Profesorado Titular De Universidad | Doctor | Bilingual | Theoretical Physics | david.brizuela@ehu.eus |
| GARAY ELIZONDO, IÑAKI | University of the Basque Country | Profesorado Agregado | Doctor | Bilingual | Theoretical Physics | inaki.garay@ehu.eus |
Competencies
| Name | Weight |
|---|---|
| Resolución de problemas | 70.0 % |
| Understanding the topics and being able to present them | 15.0 % |
| To be able to present a topic not explicitly included in the syllabus | 15.0 % |
Study types
| Type | Face-to-face hours | Non face-to-face hours | Total hours |
|---|---|---|---|
| Lecture-based | 24 | 32 | 56 |
| Seminar | 8 | 12 | 20 |
| Applied classroom-based groups | 8 | 16 | 24 |
Assessment systems
| Name | Minimum weighting | Maximum weighting |
|---|---|---|
| Oral examination | 50.0 % | 50.0 % |
| Practical tasks | 50.0 % | 50.0 % |
| Presentations | 15.0 % | 50.0 % |
| Questions to discuss | 15.0 % | 70.0 % |
Ordinary call: orientations and renunciation
In case the sanitary conditions do not allow for a face-to-face evaluation, an online evaluation willbe activated and the students will be duly informed.
Extraordinary call: orientations and renunciation
In case the sanitary conditions do not allow for a face-to-face evaluation, an online evaluation willbe activated and the students will be duly informed.
Temary
DIFFERENTIAL GEOMETRYDifferential manifolds.
Curves, tangent vectors and tangent space.
Tensor algebra.
Tensor calculus: covariant derivative, Lie derivative, geodesics.
LIE GROUPS
Introduction to group theory.
Lie groups.
Lie algebras.
Lie group representations.
FUNCTIONAL ANALYSIS
Introduction: normed linear spaces.
Banach and Hilbert spaces.
Operators and spectral theory.
Distributions and Fourier transform.
Bibliography
Basic bibliography
[1] C. Isham, Modern Differential Geometry for Physicists, World Scientific (1999).[2] T. Frankel, The Geometry of Physics: An Introduction, Cambridge University Press (2012).
[3] M. Nakahara, Geometry, Topology and Physics, CRC Press (2003).
[4] R. M. Wald, General Relativity, University Of Chicago Press (1984).
[5] R. d’Inverno, Introducing Einstein’s Relativity, Oxford University Press (1992).
[6] B. C. Hall, Lie Groups, Lie Algebras, and Representations, Springer-Verlag (2003).
[7] W. Rossmann, Lie Groups, Oxford University Press (2002).
[8] K. Erdmann, M. J. Wildon, Introduction to Lie Algebras, Springer-Verlag (2006).
[9] N. Boccara, Functional Analysis: An Introduction for Physicists, Academic Press (1990).
[10] Y. Eidelman, V. Milman, A. Tsolomitis, Functional Analysis: An Introduction, American
Mathematical Society (2000).
[11] D. Farenick, Fundamentals of Functional Analysis, Springer (2016).
[12] J. B. Conway, A Course in Functional Analysis, Springer (1990).
[13] A. Bowers, N. J. Kalton, An Introductory Course in Functional Analysis, Springer (2014).
[14] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Academic Press (1980).