Differential Geometry of Manifolds (Record no. 69838)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05145cam a2200541Mu 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780429059292 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220711211910.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 191228s2019 xx o 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429607820 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429607822 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429059292 |
| -- | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429059299 |
| -- | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780429602306 |
| -- | (electronic bk. : EPUB) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 0429602308 |
| -- | (electronic bk. : EPUB) |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 516.3/6 |
| 100 1# - AUTHOR NAME | |
| Author | Lovett, Stephen |
| 245 10 - TITLE STATEMENT | |
| Title | Differential Geometry of Manifolds |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Milton : |
| Publisher | CRC Press LLC, |
| Year of publication | 2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (451 p.). |
| 490 1# - SERIES STATEMENT | |
| Series statement | Textbooks in Mathematics Ser. |
| 500 ## - GENERAL NOTE | |
| Remark 1 | Description based upon print version of record. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Acknowledgments -- 1: Analysis of Multivariable Functions -- 1.1 Functions from ?n to ?m -- 1.2 Continuity, Limits, and Differentiability -- 1.3 Differentiation Rules -- Functions of Class Cr -- 1.4 Inverse and Implicit Function Theorems -- 2: Variable Frames -- 2.1 Frames Associated to Coordinate Systems -- 2.2 Frames Associated to Trajectories -- 2.3 Variable Frames and Matrix Functions -- 3: Differentiable Manifolds -- 3.1 Definitions and Examples |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 3.2 Differentiable Maps between Manifolds -- 3.3 Tangent Spaces -- 3.4 The Differential of a Differentiable Map -- 3.5 Manifolds with Boundaries -- 3.6 Immersions, Submersions, and Submanifolds -- 3.7 Orientability -- 4: Multilinear Algebra -- 4.1 Hom Space and Dual -- 4.2 Bilinear Forms and Inner Products -- 4.3 Adjoint, Self-Adjoint, and Automorphisms -- 4.4 Tensor Product -- 4.5 Components of Tensors over V -- 4.6 Symmetric and Alternating Products -- 4.7 Algebra over a Field -- 5: Analysis on Manifolds -- 5.1 Vector Bundles on Manifolds -- 5.2 Vector and Tensor Fields on Manifolds |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 5.3 Lie Bracket and Lie Derivative -- 5.4 Differential Forms -- 5.5 Pull-Backs of Covariant Tensor Fields -- 5.6 Lie Derivative of Tensor Fields -- 5.7 Integration on Manifolds -- Definition -- 5.8 Integration on Manifolds -- Applications -- 5.9 Stokes' Theorem -- 6: Introduction to Riemannian Geometry -- 6.1 Riemannian Metrics -- 6.2 Connections and Covariant Differentiation -- 6.3 Vector Fields along Curves -- Geodesics -- 6.4 Curvature Tensor -- 6.5 Ricci Curvature and Einstein Tensor -- 7: Applications of Manifolds to Physics -- 7.1 Hamiltonian Mechanics -- 7.2 Special Relativity |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Pseudo-Riemannian Manifolds -- 7.3 Electromagnetism -- 7.4 Geometric Concepts in String Theory -- 7.5 Brief Introduction to General Relativity -- A: Point Set Topology -- A.1 Metric Spaces -- A.2 Topological Spaces -- B: Calculus of Variations -- B.1 Formulation of Several Problems -- B.2 Euler-Lagrange Equation -- B.3 Several Dependent Variables -- B.4 Isoperimetric Problems and Lagrange Multipliers -- C: Further Topics in Multilinear Algebra -- C.1 Binet-Cauchy and k-Volume of Parallelepipeds -- C.2 Volume Form Revisited -- C.3 Hodge Star Operator -- Bibliography -- Index |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a both streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics. The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, string theory. The Second Edition of this successful textbook offers several notable points of revision. New to the Second Edition: New problems have been added and the level of challenge has been changed to the exercises Each section corresponds to a 60-minute lecture period, making it more user-friendly for lecturers Includes new sections which provide more comprehensive coverage of topics Features a new chapter on Multilinear Algebra |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.taylorfrancis.com/books/9780429059292 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 588 ## - | |
| -- | OCLC-licensed vendor bibliographic record. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Manifolds (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Geometry, Differential. |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / General |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Arithmetic |
| 650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | MATHEMATICS / Geometry / General |
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