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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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230814b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780691203706 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.36 |
| Item number |
NEE |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Needham, Tristan |
| 245 ## - TITLE STATEMENT |
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| Title |
Visual Differential Geometry and Forms : A Mathematical Drama in Five Acts |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Princeton University Press, |
| Date of publication, distribution, etc |
2021 |
| Place of publication, distribution, etc |
Princeton : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxviii, 501 p. ; |
| Other physical details |
ill., |
| Dimensions |
26 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
45.00 |
| Price type code |
USD |
| Unit of pricing |
85.50 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry . Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n -manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential forms |
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Angular-excess |
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Curvature Integra |
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| Topical term or geographic name as entry element |
Conformal |
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Einstein |
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| Topical term or geographic name as entry element |
Geodesic |
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| Topical term or geographic name as entry element |
Gravity |
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| Topical term or geographic name as entry element |
Hyperbolic plane |
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| Topical term or geographic name as entry element |
Intrinsic Geometry |
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| Topical term or geographic name as entry element |
Meusruer's Theorem |
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| Topical term or geographic name as entry element |
Poincare Hopf theorem |
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| Topical term or geographic name as entry element |
Pseudosphere |
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Rotation matrix |
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Sphere |
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Tangent vector |
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| Topical term or geographic name as entry element |
Vector field |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |