Elucidates the mathematical foundation of coordinate systems and their practical application to different branches of mathematics and natural and engineering sciences. Contains a thorough discussion of theory, and details applications taken from the fields of physics and geodesy, illustrated with examples. Treats related problems including previously unpublished numerical integration methods. Includes an extensive formulary consisting of some 40 tables on different types of coordinates, offering directly applicable information on important features in a unified notational system. For practitioners and students of science and engineering. Annotation copyright by Book News, Inc., Portland, OR
Author(s): Wolfram Neutsch
Publisher: Walter de Gruyter
Year: 1996
Language: English
Pages: 1365
City: Berlin
Tags: Mathematics; Geometry and Topology; Applied Mathematics
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
D. Reflections
15. Coxeter groups
16. Invariant rings of finite Weyl groups
17. Basic invariants
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
Index
