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Coordinates Reprint 2010 [Kõva köide]

  • Formaat: Hardback, 1378 pages, kõrgus x laius: 230x155 mm, kaal: 2323 g
  • Ilmumisaeg: 10-Oct-1996
  • Kirjastus: De Gruyter
  • ISBN-10: 3110148528
  • ISBN-13: 9783110148527
Teised raamatud teemal:
Coordinates Reprint 2010Suurem pilt
  • Formaat: Hardback, 1378 pages, kõrgus x laius: 230x155 mm, kaal: 2323 g
  • Ilmumisaeg: 10-Oct-1996
  • Kirjastus: De Gruyter
  • ISBN-10: 3110148528
  • ISBN-13: 9783110148527
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783110148527.html
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 Treats related problems including previously unpublished numerical integration methods.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 c. by Book News, Inc., Portland, Or.
Volume 1: Theory
0. Introduction
1(8)
A. Foundations 9(61)
1. Historical development of the coordinate concept
9(29)
1.1. Geography
9(6)
1.2. Affine and projective geometry
15(5)
1.3. Differential geometry
20(4)
1.4. Geodesy and cartography
24(10)
1.5. Special coordinates
34(4)
2. Notation and conventions
38(32)
2.1. Sets and topological spaces
38(4)
2.2. Groups
42(6)
2.3. Matrices
48(8)
2.4. Multilinear forms and tensors
56(9)
2.5. Polynomials
65(5)
B. Geometry 70(225)
3. Manifolds
70(43)
3.1. Continuous coordinate systems
70(3)
3.2. Smooth manifolds
73(3)
3.3. Curves and tangent spaces
76(4)
3.4. Vector bundles
80(5)
3.5. Differential and exterior derivation
85(9)
3.6. Partition of unity
94(8)
3.7. Oriented manifolds
102(4)
3.8. Integration of differential forms
106(4)
3.9. Stokes' theorem
110(3)
4. Riemannian spaces
113(47)
4.1. The metric tensor
113(4)
4.2. Christoffel symbols and covariant derivation
117(6)
4.3. Normal coordinates
123(5)
4.4. Curvature
128(8)
4.5. Volume
136(9)
4.6. Duality
145(4)
4.7. Classical vector analysis
149(11)
5. Applications to physics
160(30)
5.1. Mechanics
160(6)
5.2. Hydrodynamics
166(6)
5.3. Relativity
172(3)
5.4. Electromagnetism
175(7)
5.5. Optics
182(5)
5.6. Quantum mechanics
187(3)
6. Complex analysis
190(56)
6.1. Elementary properties of complex numbers
190(3)
6.2. Convergence of function series
193(5)
6.3. Power series
198(7)
6.4. Analytical continuation
205(6)
6.5. Holomorphic functions
211(14)
6.6. Angle-preserving transformations
225(8)
6.7. Lie groups
233(4)
6.8. Lie algebras
237(9)
7. Projective Geometry
246(49)
7.1. Affine and projective coordinates
246(9)
7.2. Projectivities
255(5)
7.3. The cross ratio
260(8)
7.4. Bezout's theorem
268(11)
7.5. Planar algebraic curves
279(8)
7.6. Stereographic projection
287(6)
7.7. Higher dimensional spaces
293(2)
C. Rotations 295(233)
8. Orthogonal groups
295(23)
8.1. Isometries and Euclidean transformations
295(6)
8.2. The exponential mapping
301(10)
8.3. Rational parametrization
311(7)
9. Linear transformations of complex spaces
318(35)
9.1. Pauli matrices
318(4)
9.2. Cayley-Klein parameters
322(5)
9.3. The angular momentum algebra
327(9)
9.4. Gaussian mutations of space
336(3)
9.5. Euler angles
339(3)
9.6. Elementary geometry of the Riemann number sphere
342(11)
10. Quaternions
353(26)
10.1. The skew field of quaternions
353(6)
10.2. Left and right multiplication
359(3)
10.3. Rotations of the quaternion algebra
362(5)
10.4. Representation by complex matrices
367(4)
10.5. Finite groups of quaternions
371(8)
11. Octaves
379(50)
11.1. Doubling method of Cayley and Dickson
379(10)
11.2. Alternative division algebras
389(15)
11.3. The theorem of Hurwitz
404(7)
11.4. Quadratic algebras
411(14)
11.5. Parallelizability and regular vielbeine
425(4)
12. Hopf mappings
429(23)
12.1. Homotopy groups of spheres
429(4)
12.2. Homotopy invariants
433(5)
12.3. Duplication of angles and classical Hopf fibration
438(6)
12.4. Generalizations
444(4)
12.5. Geometric peculiarities
448(4)
13. Spinors
452(40)
13.1. Schur extensions of the symmetric groups
452(14)
13.2. Spin groups
466(4)
13.3. Grabmann algebras
470(6)
13.4. Clifford algebras
476(10)
13.5. Dirac matrices
486(6)
14. Lorentz transformations
492(36)
14.1. The Poincare group
492(7)
14.2. Boosts
499(9)
14.3. Complex Lorentz matrices
508(8)
14.4. Description by quaternions
516(6)
14.5. Representation theory of the Lorentz group
522(6)
D. Reflections 528(109)
15. Coxeter groups
528(46)
15.1. Discrete symmetries
528(4)
15.2. Invariant theory; Molien's theorem
532(6)
15.3. Polynomial invariant rings
538(12)
15.4. Reflection groups
550(8)
15.5. Fundamental systems
558(8)
15.6. The Euclidean Coxeter groups
566(8)
16. Invariant rings of finite Weyl groups
574(31)
16.1. Root systems
574(15)
16.2. Weyl groups
589(10)
16.3. Elementary symmetric functions
599(6)
17. Basic invariants
605(32)
17.1. Generic Weyl groups (A,B,D)
605(2)
17.2. Weyl groups of type E
607(16)
17.3. Weyl groups of types F,G,H,I
623(12)
17.4. Basic degrees
635(2)
Volume 2: Applications
E. Lattices 637(200)
18. Elliptic functions and modular forms
637(51)
18.1. Doubly periodic functions
637(6)
18.2. WeierstraXXX functions
643(11)
18.3. The modular group
654(7)
18.4. Modular forms
661(11)
18.5. Cusp forms
672(6)
18.6. Modular functions; the J-invariant
678(10)
19. Euclidean lattices
688(38)
19.1. Foundations of lattice theory
688(10)
19.2. Theta functions
698(14)
19.3. The Gosset lattice
712(5)
19.4. Niemeier lattices
717(9)
20. Linear codes
726(55)
20.1. Encoding of information
726(4)
20.2. The Hexacode
730(8)
20.3. The binary Golay code
738(13)
20.4. Miracle octad generator
751(6)
20.5. Alternative constructions of the Golay code
757(10)
20.6. Steiner systems and Mathieu groups
767(14)
21. The Leech lattice
781(56)
21.1. Uniqueness of the Leech lattice
781(8)
21.2. Explicit representations
789(3)
21.3. Automorphisms
792(7)
21.4. Holes in the Leech lattice
799(7)
21.5. Invariants of the Conway group
806(13)
21.6. Lorentz lattices and sporadic groups
819(18)
F. Spheres 837(148)
22. Harmonic functions
837(29)
22.1. The theorems of Green
837(7)
22.2. Dirichlet's principle
844(10)
22.3. The Poisson integral
854(8)
22.4. Potential functions
862(4)
23. Spherical surface functions
866(47)
23.1. Spherical harmonics
866(4)
23.2. Legendre polynomials
870(11)
23.3. Orthogonal functions on the 2-sphere
881(16)
23.4. Clebsch-Gordan coefficients
897(16)
24. Lattice integration
913(32)
24.1. Integration points and weights
913(7)
24.2. Numerical integration after GauB
920(8)
24.3. Simple examples
928(7)
24.4. Integration by means of the Gosset lattice
935(6)
24.5. Transfer via Hopf mappings
941(4)
25. Spherical designs
945(40)
25.1. Integration methods with equal weights
945(6)
25.2. Tight designs
951(5)
25.3. Optimal integration on the 2-sphere
956(10)
25.4. The hypersphere
966(10)
25.5. Very high precision numerical integration
976(5)
25.6. Four-dimensional root systems and quaternions
981(4)
G. Coordinate systems 985(147)
26. Linear and reducible coordinates
985(21)
26.1. Cartesian and oblique linear frames
985(6)
26.2. Polar coordinates
991(4)
26.3. Classical cylindrical coordinates
995(2)
26.4. Separable isothermal systems
997(9)
27. Three-dimensional Stackel coordinates
1006(31)
27.1. Rotational symmetry
1006(9)
27.2. Stackel spaces
1015(5)
27.3. Classification of Stackel-type metrics
1020(9)
27.4. Bipolar coordinates
1029(8)
28. Confocal Coordinates
1037(31)
28.1. Orthogonal families of quadrics
1037(8)
28.2. Metric and differential operators
1045(8)
28.3. Separation of the potential equation
1053(5)
28.4. Lame functions
1058(6)
28.5. Geodesics on the ellipsoid
1064(4)
29. GauB-Kruger Coordinates
1068(36)
29.1. Soldner's parameterization of the spheroid
1068(9)
29.2. Series expansions
1077(6)
29.3. Transversal Mercator projection
1083(12)
29.4. Bessel's figure of the Earth
1095(5)
29.5. Recent models
1100(4)
30. Coordinates for special applications
1104(28)
30.1. Clairaut coordinates
1104(5)
30.2. Roche coordinates
1109(4)
30.3. Planar Weyl coordinates
1113(5)
30.4. Weyl coordinates in three-dimensional space
1118(8)
30.5. Higher dimensional Weyl coordinates
1126(6)
H. Tables 1132(165)
Calculation and organization of the tables
1132(4)
Coordinates in R(2)
1136(35)
Cartesian coordinates
1136(3)
Polar coordinates
1139(3)
Parabolic coordinates
1142(3)
Elliptic coordinates
1145(3)
Confocal coordinates
1148(4)
Bipolar coordinates
1152(4)
Digonal coordinates
1156(3)
Trigonal coordinates
1159(3)
Tetragonal coordinates
1162(3)
Pentagonal coordinates
1165(3)
Hexagonal coordinates
1168(3)
Coordinates in R(3)
1171(94)
Cartesian coordinates
1171(3)
Cylindrical coordinates
1174(4)
Polar coordinates
1178(4)
Geographic coordinates
1182(4)
Coordinates of the parabolic cylinder
1186(4)
Coordinates of the elliptic cylinder
1190(4)
Confocal cylindrical coordinates
1194(4)
Coordinates of the circular paraboloid
1198(4)
Coordinates of the elliptic paraboloid
1202(5)
Ellipsoidal coordinates (prolate)
1207(4)
Ellipsoidal coordinates (oblate)
1211(4)
Spheroidal coordinates (prolate)
1215(4)
Spheroidal coordinates (oblate)
1219(4)
Conical coordinates
1223(5)
Confocal coordinates
1228(6)
Bicylindrical coordinates
1234(4)
Bispherical coordinates
1238(5)
Torus coordinates
1243(5)
Tetrahedral coordinates
1248(5)
Octahedral coordinates
1253(6)
Ocosahedral coordinates
1259(6)
Coordinates in R(4)
1265(32)
Cartesian coordinates
1265(3)
Cylindrical coordinates of type (1,3)
1268(4)
Cylindrical coordinates of type (2,2)
1272(4)
Polar coordinates
1276(4)
Geographic coordinates
1280(4)
Double polar coordinates
1284(4)
Confocal coordinates
1288(9)
Appendix 1297(25)
References 1297(25)
Index 1322