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Functional Differential Geometry [Hardback]

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, , With (Northwestern University)
  • Formāts: Hardback, 248 pages, height x width x depth: 229x152x11 mm, weight: 449 g, 8 b&w illus.
  • Sērija : Functional Differential Geometry
  • Izdošanas datums: 05-Jul-2013
  • Izdevniecība: MIT Press
  • ISBN-10: 0262019345
  • ISBN-13: 9780262019347
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 70,32 €
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Functional Differential GeometryPalielināt
  • Formāts: Hardback, 248 pages, height x width x depth: 229x152x11 mm, weight: 449 g, 8 b&w illus.
  • Sērija : Functional Differential Geometry
  • Izdošanas datums: 05-Jul-2013
  • Izdevniecība: MIT Press
  • ISBN-10: 0262019345
  • ISBN-13: 9780262019347
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780262019347.html
Keywords:
An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.

Preface xi
Prologue xv
1 Introduction
1(10)
2 Manifolds
11(10)
2.1 Coordinate Functions
12(2)
2.2 Manifold Functions
14(7)
3 Vector Fields and One-Form Fields
21(20)
3.1 Vector Fields
21(5)
3.2 Coordinate-Basis Vector Fields
26(3)
3.3 Integral Curves
29(3)
3.4 One-Form Fields
32(2)
3.5 Coordinate-Basis One-Form Fields
34(7)
4 Basis Fields
41(14)
4.1 Change of Basis
44(3)
4.2 Rotation Basis
47(1)
4.3 Commutators
48(7)
5 Integration
55(16)
5.1 Higher Dimensions
57(5)
5.2 Exterior Derivative
62(3)
5.3 Stokes's Theorem
65(2)
5.4 Vector Integral Theorems
67(4)
6 Over a Map
71(12)
6.1 Vector Fields Over a Map
71(2)
6.2 One-Form Fields Over a Map
73(1)
6.3 Basis Fields Over a Map
74(2)
6.4 Pullbacks and Pushforwards
76(7)
7 Directional Derivatives
83(32)
7.1 Lie Derivative
85(8)
7.2 Covariant Derivative
93(11)
7.3 Parallel Transport
104(7)
7.4 Geodesic Motion
111(4)
8 Curvature
115(18)
8.1 Explicit Transport
116(8)
8.2 Torsion
124(1)
8.3 Geodesic Deviation
125(4)
8.4 Bianchi Identities
129(4)
9 Metrics
133(20)
9.1 Metric Compatibility
135(2)
9.2 Metrics and Lagrange Equations
137(7)
9.3 General Relativity
144(9)
10 Hodge Star and Electrodynamics
153(14)
10.1 The Wave Equation
159(1)
10.2 Electrodynamics
160(7)
11 Special Relativity
167(18)
11.1 Lorentz Transformations
172(7)
11.2 Special Relativity Frames
179(2)
11.3 Twin Paradox
181(4)
A Scheme 185(10)
B Our Notation 195(16)
C Tensors 211(6)
References 217(2)
Index 219