| 000 -LEADER |
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| fixed length control field |
a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
230901b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783030456528 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.07 |
| Item number |
NES |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Nestruev, Jet |
| 245 ## - TITLE STATEMENT |
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| Title |
Smooth manifolds and observables |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2020 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 433 p. ; |
| Other physical details |
ill., |
| Dimensions |
24 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
49.99 |
| Price type code |
EUR |
| Unit of pricing |
94.90 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Graduate texts in mathematics |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from classical physics. A broad audience will appreciate this unique approach for the insight it gives into the underlying connections between geometry, physics, and commutative algebra. The main objective of this book is to explain how differential calculus is a natural part of commutative algebra. This is achieved by studying the corresponding algebras of smooth functions that result in a general construction of the differential calculus on various categories of modules over the given commutative algebra. It is shown in detail that the ordinary differential calculus and differential geometry on smooth manifolds turns out to be precisely the particular case that corresponds to the category of geometric modules over smooth algebras. This approach opens the way to numerous applications, ranging from delicate questions of algebraic geometry to the theory of elementary particles. Smooth Manifolds and Observables is intended for advanced undergraduates, graduate students, and researchers in mathematics and physics. This second edition adds ten new chapters to further develop the notion of differential calculus over commutative algebras, showing it to be a generalization of the differential calculus on smooth manifolds. Applications to diverse areas, such as symplectic manifolds, de Rham cohomology, and Poisson brackets are explored. Additional examples of the basic functors of the theory are presented alongside numerous new exercises, providing readers with many more opportunities to practice these concepts. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra |
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| Topical term or geographic name as entry element |
Analytic geometry |
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| Topical term or geographic name as entry element |
Mathematics Topology |
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| Topical term or geographic name as entry element |
Quantum physics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |