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040 _aOCoLC-P
_beng
_cOCoLC-P
020 _a9780429607820
020 _a0429607822
020 _a9780429059292
_q(electronic bk.)
020 _a0429059299
_q(electronic bk.)
020 _a9780429602306
_q(electronic bk. : EPUB)
020 _a0429602308
_q(electronic bk. : EPUB)
035 _a(OCoLC)1132420688
035 _a(OCoLC-P)1132420688
050 4 _aQA649
072 7 _aMAT
_x000000
_2bisacsh
072 7 _aMAT
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072 7 _aMAT
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072 7 _aPBM
_2bicssc
082 0 4 _a516.3/6
100 1 _aLovett, Stephen
_q(Stephen T.)
245 1 0 _aDifferential Geometry of Manifolds
_h[electronic resource].
250 _a2nd ed.
260 _aMilton :
_bCRC Press LLC,
_c2019.
300 _a1 online resource (451 p.).
490 1 _aTextbooks in Mathematics Ser.
500 _aDescription based upon print version of record.
505 0 _aCover -- 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 _a3.2 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 _a5.3 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 _aPseudo-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 _aDifferential 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
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aManifolds (Mathematics)
650 0 _aGeometry, Differential.
650 7 _aMATHEMATICS / General
_2bisacsh
650 7 _aMATHEMATICS / Arithmetic
_2bisacsh
650 7 _aMATHEMATICS / Geometry / General
_2bisacsh
856 4 0 _3Read Online
_uhttps://www.taylorfrancis.com/books/9780429059292
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _2lcc
_cEBK
999 _c17361
_d17361