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Mathematics of Relativity [Minkštas viršelis]

  • Formatas: Paperback / softback, 192 pages, aukštis x plotis x storis: 228x10x151 mm, weight: 261 g
  • Serija: Dover Books on Physics
  • Išleidimo metai: 26-Dec-2014
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486783251
  • ISBN-13: 9780486783253
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 192 pages, aukštis x plotis x storis: 228x10x151 mm, weight: 261 g
  • Serija: Dover Books on Physics
  • Išleidimo metai: 26-Dec-2014
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486783251
  • ISBN-13: 9780486783253
Kitos knygos pagal šią temą:
Writing for graduate and advanced graduate students of physics, Rainich introduces the mathematics of relativity by treating the difficult parts one by one in a staged progression. He begins with the familiar inverse square law in terms of simple calculus, then introduces step by step more complicated situations, gradually bringing in more sophisticated mathematical tools. Not until the need arises does he bring in changes in fundamental concepts that characterize the theory of relativity, or refinements of the mathematical techniques. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Concise treatment, based on ideas of Einstein and Minkowski, geared toward advanced undergraduates and graduate students of physics. Topics include old physics, new geometry, special relativity, curved space, and general relativity. 1950 edition.


Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity.
Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor.
1 OLD PHYSICS
1(25)
1 Motion of a Particle. The Inverse Square Law
1(5)
2 Two Pictures of Matter
6(4)
3 Vectors, Tensors, Operations
10(3)
4 Maxwell's Equations
13(7)
5 The Stress-Energy Tensor
20(3)
6 General Equations of Motion. The Complete Tensor
23(3)
2 NEW GEOMETRY
26(44)
7 Analytic Geometry of Four Dimensions
26(6)
8 Transformation of Coordinates
32(4)
9 Postulates for Four-Dimensional Geometry
36(3)
10 Tensor Analysis
39(12)
11 Complications Resulting from Imaginary Coordinate
51(13)
12 Are the Equations of Physics Invariant?
64(2)
13 Curves in the New Geometry
66(4)
3 SPECIAL RELATIVITY
70(29)
14 Equations of Motion
70(6)
15 Lorentz Transformations
76(4)
16 Addition of Velocities
80(2)
17 Light Corpuscles, or Photons
82(6)
18 Electricity and Magnetism in Special Relativity
88(2)
19 The Complete Tensor
90(9)
4 CURVED SPACE
99(46)
20 Curvature of Curves and Surfaces
101(5)
21 Generalizations
106(3)
22 The Riemann Tensor
109(4)
23 Points and Vectors in General Coordinates
113(3)
24 Tensors in General Coordinates
116(5)
25 Differentiation in General Coordinates
121(6)
26 General Coordinates in Curved Spaces
127(6)
27 Riemann Tensor in General Coordinates
133(4)
28 Geodesics
137(4)
29 Equations of Physics in General Coordinates
141(4)
5 GENERAL RELATIVITY
145(24)
30 The Law of Geodesics
146(2)
31 Solar System. Symmetry Conditions
148(4)
32 Solution of the Field Equations
152(3)
33 Equations of Geodesics
155(1)
34 Newtonian Motion of a Planet
156(3)
35 Relativity Motion of a Planet
159(3)
36 Deflection of Light
162(2)
37 Shift of Spectral Lines
164(5)
Conclusion 169(2)
Index 171