1. Complex numbers
2. Holomorphic functions
3. Cauchy's theorem
4. Cauchy's integral formulae
5. Residue theorem
6. Conical intersections and the molecular Berry phase
7. Taylor series
8. Laurent series
9. Classification of singularities: poles vs. essential singularities vs. removable singularities
10. Optical spectra as poles of the response function
11. Photoemission and inverse photoemission spectra as poles of the Green function
12. Causality and Kramers-Kronig relations
13. Functionals
14. The basic idea of density functional theory
15. The functional derivative
16. Variational principles in chemistry and physics
2. Holomorphic functions
3. Cauchy's theorem
4. Cauchy's integral formulae
5. Residue theorem
6. Conical intersections and the molecular Berry phase
7. Taylor series
8. Laurent series
9. Classification of singularities: poles vs. essential singularities vs. removable singularities
10. Optical spectra as poles of the response function
11. Photoemission and inverse photoemission spectra as poles of the Green function
12. Causality and Kramers-Kronig relations
13. Functionals
14. The basic idea of density functional theory
15. The functional derivative
16. Variational principles in chemistry and physics
- Teacher: Eberhard Gross