Coordinates (PDF)

I-XIV -- Volume 1: Theory -- 0. Introduction -- A. Foundations. -- 1. Historical development of the coordinate concept -- 2. Notation and conventions -- B. Geometry. -- 3. Manifolds -- 4. Riemannian spaces -- 5. Applications to physics -- 6. Complex analysis -- 7. Projective Geometry -- C. Rotations. -- 8. Orthogonal groups -- 9. Linear transformations of complex spaces -- 10. Quaternions -- 11. Octaves -- 12. Hopf mappings -- 13. Spinors -- 14. Lorentz transformations -- 15. Coxeter groups -- 16. Invariant rings of finite Weyl groups -- 17. Basic invariants -- Volume 2: Applications -- E. Lattices. -- 18. Elliptic functions and modular forms -- 19. Euclidean lattices -- 20. Linear codes -- 21. The Leech lattice -- F. Spheres. -- 22. Harmonic functions -- 23. Spherical surface functions -- 24. Lattice integration -- 25. Spherical designs -- G. Coordinate systems. -- 26. Linear and reducible coordinates -- 27. Three-dimensional Stackel coordinates -- 28. Confocal Coordinates -- 29. Gauss-Krüger Coordinates -- 30. Coordinates for special applications -- H. Tables. -- Calculation and organization of the tables -- Coordinates in R2 -- Coordinates in R3 -- Coordinates in R4 -- Appendix. References -- Appendix. Index