MARC details
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03427nam a22003257a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20240626112301.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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240625b |||||||| |||| 00| 0 hin d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319855622 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
NISER LIBRARY |
| Language of cataloging |
eng |
| Transcribing agency |
NISER LIBRARY |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
English |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
514.7 |
| Item number |
TU-D |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Tu, Loring W. |
| 245 10 - TITLE STATEMENT |
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| Title |
Differential geometry : |
| Remainder of title |
connections, curvature, and characteristic classes |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
Switzerland : |
| Name of publisher, distributor, etc. |
Springer, |
| Date of publication, distribution, etc. |
2017. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xvi, 346p. : |
| Other physical details |
87 illustrations, 15 illustrations in color. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Graduate texts in mathematics |
| Volume/sequential designation |
275 |
| International Standard Serial Number |
0072-5285 ; |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text.<br/>Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.<br/><br/>Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic geometry. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential geometry. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Christoffel symbols |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Codazzi–Mainardi equation |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Gauss Curvature equation |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Gauss Theorema egregium |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Gauss–Bonnet theorem |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Gram–Schmidt process |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Table of Contents |
| Uniform Resource Identifier |
<a href="https://link.springer.com/content/pdf/bfm:978-3-319-55084-8/1">https://link.springer.com/content/pdf/bfm:978-3-319-55084-8/1</a> |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Reviews |
| Uniform Resource Identifier |
<a href="https://www.goodreads.com/book/show/45428935-differential-geometry?ref=nav_sb_ss_1_13#CommunityReviews">https://www.goodreads.com/book/show/45428935-differential-geometry?ref=nav_sb_ss_1_13#CommunityReviews</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
NBHM Books |
| Source of classification or shelving scheme |
Universal Decimal Classification |
