000			05145cam a2200541Mu 4500
001			9780429059292
003			FlBoTFG
005			20220711211910.0
006			m d
007			cr cnu---unuuu
008			191228s2019 xx o 000 0 eng d
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 _x004000 _2bisacsh
072		7	_aMAT _x012000 _2bisacsh
072		7	_aPBM _2bicssc
082	0	4	_a516.3/6
100	1		_aLovett, Stephen _q(Stephen T.) _910954
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) _910955
650		0	_aGeometry, Differential. _910956
650		7	_aMATHEMATICS / General _2bisacsh _910957
650		7	_aMATHEMATICS / Arithmetic _2bisacsh _910958
650		7	_aMATHEMATICS / Geometry / General _2bisacsh _910959
856	4	0	_3Taylor & Francis _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			_cEBK
999			_c69838 _d69838