An introduction to smooth manifolds:
Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of example...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
Springer
[2023]
|
| Schlagworte: | |
| Zusammenfassung: | Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra |
| Beschreibung: | Preface; 1 Calculus on Rn.5; 1.1 Smooth Functions. 5; 1.2 Tangent Vector. 15; 1.3 Germ of a Function. 19; 1.4 Inverse Function Theorem. 23; 1.5 Implicit Function Theorem. 36; 2 Manifold Theory 47; 2.1 Topological Manifold. 47; 2.2 Smooth Germs on a topological manifold. 55; 2.3 Smooth Manifold. 64; 2.4 Stereographic Projection. 75; iii; iv CONTENTS; 2.5 Orientable Surface. 79; 2.6 Product Manifold. 82; 2.7 Smooth Function on Smooth Manifold. 84; 2.8 Differential Curve, Tangent Vector. 91; 2.9 Inverse Function Theorem for Smooth Manifold. 97; 2.10 Vector Field. 102; 2.11 Integral Curve. 109; 2.12 Differential of a Mapping. 117; 2.13 Submanifolds. 137; 2.14 f-related vector fields. 144; 2.15 One Parameter Group of Transformations on a Manifold. 149 |
| Beschreibung: | xv, 210 Seiten Illustrationen, Diagramme 512 grams |
| ISBN: | 9789819905645 |
Internformat
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| 245 | 1 | 0 | |a An introduction to smooth manifolds |c Manjusha Majumdar, Arindam Bhattacharyya |
| 264 | 1 | |a Singapore |b Springer |c [2023] | |
| 300 | |a xv, 210 Seiten |b Illustrationen, Diagramme |c 512 grams | ||
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| 500 | |a Preface; 1 Calculus on Rn.5; 1.1 Smooth Functions. 5; 1.2 Tangent Vector. 15; 1.3 Germ of a Function. 19; 1.4 Inverse Function Theorem. 23; 1.5 Implicit Function Theorem. 36; 2 Manifold Theory 47; 2.1 Topological Manifold. 47; 2.2 Smooth Germs on a topological manifold. 55; 2.3 Smooth Manifold. 64; 2.4 Stereographic Projection. 75; iii; iv CONTENTS; 2.5 Orientable Surface. 79; 2.6 Product Manifold. 82; 2.7 Smooth Function on Smooth Manifold. 84; 2.8 Differential Curve, Tangent Vector. 91; 2.9 Inverse Function Theorem for Smooth Manifold. 97; 2.10 Vector Field. 102; 2.11 Integral Curve. 109; 2.12 Differential of a Mapping. 117; 2.13 Submanifolds. 137; 2.14 f-related vector fields. 144; 2.15 One Parameter Group of Transformations on a Manifold. 149 | ||
| 520 | |a Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra | ||
| 650 | 4 | |a bicssc | |
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| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Topological groups | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Geometry, Differential | |
| 653 | |a Hardcover, Softcover / Mathematik/Geometrie | ||
| 700 | 1 | |a Bhattacharyya, Arindam |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-981-99-0565-2 |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034290675 | ||
Datensatz im Suchindex
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| id | DE-604.BV049027914 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:15:40Z |
| indexdate | 2024-07-10T09:53:12Z |
| institution | BVB |
| isbn | 9789819905645 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034290675 |
| oclc_num | 1401182847 |
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| owner_facet | DE-29T |
| physical | xv, 210 Seiten Illustrationen, Diagramme 512 grams |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Springer |
| record_format | marc |
| spelling | Majumdar, Manjusha Verfasser aut An introduction to smooth manifolds Manjusha Majumdar, Arindam Bhattacharyya Singapore Springer [2023] xv, 210 Seiten Illustrationen, Diagramme 512 grams txt rdacontent n rdamedia nc rdacarrier Preface; 1 Calculus on Rn.5; 1.1 Smooth Functions. 5; 1.2 Tangent Vector. 15; 1.3 Germ of a Function. 19; 1.4 Inverse Function Theorem. 23; 1.5 Implicit Function Theorem. 36; 2 Manifold Theory 47; 2.1 Topological Manifold. 47; 2.2 Smooth Germs on a topological manifold. 55; 2.3 Smooth Manifold. 64; 2.4 Stereographic Projection. 75; iii; iv CONTENTS; 2.5 Orientable Surface. 79; 2.6 Product Manifold. 82; 2.7 Smooth Function on Smooth Manifold. 84; 2.8 Differential Curve, Tangent Vector. 91; 2.9 Inverse Function Theorem for Smooth Manifold. 97; 2.10 Vector Field. 102; 2.11 Integral Curve. 109; 2.12 Differential of a Mapping. 117; 2.13 Submanifolds. 137; 2.14 f-related vector fields. 144; 2.15 One Parameter Group of Transformations on a Manifold. 149 Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra bicssc bisacsh Global analysis (Mathematics) Manifolds (Mathematics) Topological groups Lie groups Geometry, Differential Hardcover, Softcover / Mathematik/Geometrie Bhattacharyya, Arindam Verfasser aut Erscheint auch als Online-Ausgabe 978-981-99-0565-2 |
| spellingShingle | Majumdar, Manjusha Bhattacharyya, Arindam An introduction to smooth manifolds bicssc bisacsh Global analysis (Mathematics) Manifolds (Mathematics) Topological groups Lie groups Geometry, Differential |
| title | An introduction to smooth manifolds |
| title_auth | An introduction to smooth manifolds |
| title_exact_search | An introduction to smooth manifolds |
| title_exact_search_txtP | An introduction to smooth manifolds |
| title_full | An introduction to smooth manifolds Manjusha Majumdar, Arindam Bhattacharyya |
| title_fullStr | An introduction to smooth manifolds Manjusha Majumdar, Arindam Bhattacharyya |
| title_full_unstemmed | An introduction to smooth manifolds Manjusha Majumdar, Arindam Bhattacharyya |
| title_short | An introduction to smooth manifolds |
| title_sort | an introduction to smooth manifolds |
| topic | bicssc bisacsh Global analysis (Mathematics) Manifolds (Mathematics) Topological groups Lie groups Geometry, Differential |
| topic_facet | bicssc bisacsh Global analysis (Mathematics) Manifolds (Mathematics) Topological groups Lie groups Geometry, Differential |
| work_keys_str_mv | AT majumdarmanjusha anintroductiontosmoothmanifolds AT bhattacharyyaarindam anintroductiontosmoothmanifolds |