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20920448 |
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20230221112126.0 |
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190408s2019 nju ob 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2019016822 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119517542 (Adobe PDF) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119517559 (ePub) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781119517535 (hardcover) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119517566 |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng. |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
pcc |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA671 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.3/73 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Preferred name for the person |
Newman, Stephen C., |
| Dates associated with a name |
1952- |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Semi-Riemannian geometry : |
| Remainder of title |
the mathematical language of general relativity / |
| Statement of responsibility, etc |
Stephen C. Newman. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Hoboken, New Jersey : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
[2019] |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
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txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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computer |
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n |
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rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
nc |
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rdacarrier |
| 500 ## - GENERAL NOTE |
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| General note |
ABOUT THE AUTHOR<br/>STEPHEN C. NEWMAN is Professor Emeritus at the University of Alberta, Edmonton, Alberta, Canada. He is the author of Biostatistical Methods in Epidemiology and A Classical Introduction to Galois Theory, both published by Wiley. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 ## - CONTENTS |
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| Formatted contents note |
TABLE OF CONTENTS<br/>I Preliminaries 1<br/><br/>1 Vector Spaces 5<br/><br/>1.1 Vector Spaces 5<br/><br/>1.2 Dual Spaces 17<br/><br/>1.3 Pullback of Covectors 19<br/><br/>1.4 Annihilators 20<br/><br/>2 Matrices and Determinants 23<br/><br/>2.1 Matrices 23<br/><br/>2.2 Matrix Representations 27<br/><br/>2.3 Rank of Matrices 32<br/><br/>2.4 Determinant of Matrices 33<br/><br/>2.5 Trace and Determinant of Linear Maps 43<br/><br/>3 Bilinear Functions 45<br/><br/>3.1 Bilinear Functions 45<br/><br/>3.2 Symmetric Bilinear Functions 49<br/><br/>3.3 Flat Maps and Sharp Maps 51<br/><br/>4 Scalar Product Spaces 57<br/><br/>4.1 Scalar Product Spaces 57<br/><br/>4.2 Orthonormal Bases 62<br/><br/>4.3 Adjoints 65<br/><br/>4.4 Linear Isometries 68<br/><br/>4.5 Dual Scalar Product Spaces 72<br/><br/>4.6 Inner Product Spaces 75<br/><br/>4.7 Eigenvalues and Eigenvectors 81<br/><br/>4.8 Lorentz Vector Spaces 84<br/><br/>4.9 Time Cones 91<br/><br/>5 Tensors on Vector Spaces 97<br/><br/>5.1 Tensors 97<br/><br/>5.2 Pullback of Covariant Tensors 103<br/><br/>5.3 Representation of Tensors 104<br/><br/>5.4 Contraction of Tensors 106<br/><br/>6 Tensors on Scalar Product Spaces 113<br/><br/>6.1 Contraction of Tensors 113<br/><br/>6.2 Flat Maps 114<br/><br/>6.3 Sharp Maps 119<br/><br/>6.4 Representation of Tensors 123<br/><br/>6.5 Metric Contraction of Tensors 127<br/><br/>6.6 Symmetries of (0, 4)-Tensors 129<br/><br/>7 Multicovectors 133<br/><br/>7.1 Multicovectors 133<br/><br/>7.2 Wedge Products 137<br/><br/>7.3 Pullback of Multicovectors 144<br/><br/>7.4 Interior Multiplication 148<br/><br/>7.5 Multicovector Scalar Product Spaces 150<br/><br/>8 Orientation 155<br/><br/>8.1 Orientation of Rm 155<br/><br/>8.2 Orientation of Vector Spaces 158<br/><br/>8.3 Orientation of Scalar Product Spaces 163<br/><br/>8.4 Vector Products 166<br/><br/>8.5 Hodge Star 178<br/><br/>9 Topology 183<br/><br/>9.1 Topology 183<br/><br/>9.2 Metric Spaces 193<br/><br/>9.3 Normed Vector Spaces 195<br/><br/>9.4 Euclidean Topology on Rm 195<br/><br/>10 Analysis in Rm 199<br/><br/>10.1 Derivatives 199<br/><br/>10.2 Immersions and Diffeomorphisms 207<br/><br/>10.3 Euclidean Derivative and Vector Fields 209<br/><br/>10.4 Lie Bracket 213<br/><br/>10.5 Integrals 218<br/><br/>10.6 Vector Calculus 221<br/><br/>II Curves and Regular Surfaces 223<br/><br/>11 Curves and Regular Surfaces in R3 225<br/><br/>11.1 Curves in R3 225<br/><br/>11.2 Regular Surfaces in R3 226<br/><br/>11.3 Tangent Planes in R3 237<br/><br/>11.4 Types of Regular Surfaces in R3 240<br/><br/>11.5 Functions on Regular Surfaces in R3 246<br/><br/>11.6 Maps on Regular Surfaces in R3 248<br/><br/>11.7 Vector Fields along Regular Surfaces in R3 252<br/><br/>12 Curves and Regular Surfaces in R3v 255<br/><br/>12.1 Curves in R3v 256<br/><br/>12.2 Regular Surfaces in R3v 257<br/><br/>12.3 Induced Euclidean Derivative in R3v 266<br/><br/>12.4 Covariant Derivative on Regular Surfaces in R3v 274<br/><br/>12.5 Covariant Derivative on Curves in R3v 282<br/><br/>12.6 Lie Bracket in R3v 285<br/><br/>12.7 Orientation in R3v 288<br/><br/>12.8 Gauss Curvature in R3v 292<br/><br/>12.9 Riemann Curvature Tensor in R3v 299<br/><br/>12.10 Computations for Regular Surfaces in R3v 310<br/><br/>13 Examples of Regular Surfaces 321<br/><br/>13.1 Plane in R30 321<br/><br/>13.2 Cylinder in R30 322<br/><br/>13.3 Cone in R30 323<br/><br/>13.4 Sphere in R30 324<br/><br/>13.5 Tractoid in R30 325<br/><br/>13.6 Hyperboloid of One Sheet in R30 326<br/><br/>13.7 Hyperboloid of Two Sheets in R30 327<br/><br/>13.8 Torus in R30 329<br/><br/>13.9 Pseudosphere in R31 330<br/><br/>13.10 Hyperbolic Space in R31 331<br/><br/>III Smooth Manifolds and Semi-Riemannian Manifolds 333<br/><br/>14 Smooth Manifolds 337<br/><br/>14.1 Smooth Manifolds 337<br/><br/>14.2 Functions and Maps 340<br/><br/>14.3 Tangent Spaces 344<br/><br/>14.4 Differential of Maps 351<br/><br/>14.5 Differential of Functions 353<br/><br/>14.6 Immersions and Diffeomorphisms 357<br/><br/>14.7 Curves 358<br/><br/>14.8 Submanifolds 360<br/><br/>14.9 Parametrized Surfaces 364<br/><br/>15 Fields on Smooth Manifolds 367<br/><br/>15.1 Vector Fields 367<br/><br/>15.2 Representation of Vector Fields 372<br/><br/>15.3 Lie Bracket 374<br/><br/>15.4 Covector Fields 376<br/><br/>15.5 Representation of Covector Fields 379<br/><br/>15.6 Tensor Fields 382<br/><br/>15.7 Representation of Tensor Fields 385<br/><br/>15.8 Differential Forms 387<br/><br/>15.9 Pushforward and Pullback of Functions 389<br/><br/>15.10 Pushforward and Pullback of Vector Fields 391<br/><br/>15.11 Pullback of Covector Fields 393<br/><br/>15.12 Pullback of Covariant Tensor Fields 398<br/><br/>15.13 Pullback of Differential Forms 401<br/><br/>15.14 Contraction of Tensor Fields 405<br/><br/>16 Differentiation and Integration on Smooth Manifolds 407<br/><br/>16.1 Exterior Derivatives 407<br/><br/>16.2 Tensor Derivations 413<br/><br/>16.3 Form Derivations 417<br/><br/>16.4 Lie Derivative 419<br/><br/>16.5 Interior Multiplication 423<br/><br/>16.6 Orientation 425<br/><br/>16.7 Integration of Differential Forms 432<br/><br/>16.8 Line Integrals 435<br/><br/>16.9 Closed and Exact Covector Fields 437<br/><br/>16.10 Flows 443<br/><br/>17 Smooth Manifolds with Boundary 449<br/><br/>17.1 Smooth Manifolds with Boundary 449<br/><br/>17.2 Inward-Pointing and Outward-Pointing Vectors 452<br/><br/>17.3 Orientation of Boundaries 456<br/><br/>17.4 Stokes's Theorem 459<br/><br/>18 Smooth Manifolds with a Connection 463<br/><br/>18.1 Covariant Derivatives 463<br/><br/>18.2 Christoffel Symbols 466<br/><br/>18.3 Covariant Derivative on Curves 472<br/><br/>18.4 Total Covariant Derivatives 476<br/><br/>18.5 Parallel Translation 479<br/><br/>18.6 Torsion Tensors 485<br/><br/>18.7 Curvature Tensors 488<br/><br/>18.8 Geodesics 497<br/><br/>18.9 Radial Geodesics and Exponential Maps 502<br/><br/>18.10 Normal Coordinates 507<br/><br/>18.11 Jacobi Fields 509<br/><br/>19 Semi-Riemannian Manifolds 515<br/><br/>19.1 Semi-Riemannian Manifolds 515<br/><br/>19.2 Curves 519<br/><br/>19.3 Fundamental Theorem of Semi-Riemannian Manifolds 519<br/><br/>19.4 Flat Maps and Sharp Maps 526<br/><br/>19.5 Representation of Tensor Fields 529<br/><br/>19.6 Contraction of Tensor Fields 532<br/><br/>19.7 Isometries 535<br/><br/>19.8 Riemann Curvature Tensor 539<br/><br/>19.9 Geodesics 546<br/><br/>19.10 Volume Forms 550<br/><br/>19.11 Orientation of Hypersurfaces 551<br/><br/>19.12 Induced Connections 558<br/><br/>20 Differential Operators on Semi-Riemannian Manifolds 561<br/><br/>20.1 Hodge Star 561<br/><br/>20.2 Codifferential 562<br/><br/>20.3 Gradient 566<br/><br/>20.4 Divergence of Vector Fields 568<br/><br/>20.5 Curl 572<br/><br/>20.6 Hesse Operator 573<br/><br/>20.7 Laplace Operator 575<br/><br/>20.8 Laplace-de Rham Operator 576<br/><br/>20.9 Divergence of Symmetric 2-Covariant Tensor Fields 577<br/><br/>21 Riemannian Manifolds 579<br/><br/>21.1 Geodesics and Curvature on Riemannian Manifolds 579<br/><br/>21.2 Classical Vector Calculus Theorems 582<br/><br/>22 Applications to Physics 587<br/><br/>22.1 Linear Isometries on Lorentz Vector Spaces 587<br/><br/>22.2 Maxwell's Equations 598<br/><br/>22.3 Einstein Tensor 603<br/><br/>IV Appendices 609<br/><br/>A Notation and Set Theory 611<br/><br/>B Abstract Algebra 617<br/><br/>B.1 Groups 617<br/><br/>B.2 Permutation Groups 618<br/><br/>B.3 Rings 623<br/><br/>B.4 Fields 623<br/><br/>B.5 Modules 624<br/><br/>B.6 Vector Spaces 625<br/><br/>B.7 Lie Algebras 626<br/><br/>Further Reading 627<br/><br/>Index 629 |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
An introduction to semi-Riemannian geometry as a foundation for general relativity<br/><br/>Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
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| Source of description note |
Description based on print version record and CIP data provided by publisher; resource not viewed. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Semi-Riemannian geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Geometry, Riemannian. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Manifolds (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry, Differential. |
| 655 #0 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Link text |
Full text available at Wiley Online Library Click here to view |
| Uniform Resource Identifier |
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119517566 |
| 942 ## - ADDED ENTRY ELEMENTS |
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| Source of classification or shelving scheme |
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| Item type |
EBOOK |