000			00351nam a2200133Ia 4500
999			_c179836 _d179836
020			_a0262019345
040			_cCUS
082			_a516.36 _bSUS/F
100			_aSussman, Gerald Jay
245		0	_aFunctional differential geometry/ _cGerald Jay Sussman
260			_aLondon: _bThe MIT Press, _c2013-07-05.
300			_a228p.
505			_a2.1 Coordinate Functions 12 2.2 Manifold Functions 14 3 Vector Fields and One-Form Fields 21 3.1 Vector Fields 21 3.2 Coordinate-Basis Vector Fields 26 3.3 Integral Curves 29 3.4 One-Form Fields 32 3.5 Coordinate-Basis One-Form Fields 34 4 Basis Fields 41 4.1 Change of Basis 44 4.2 Rotation Basis 47 4.3 Commutators 48 5 Integration 55 5.1 Higher Dimensions 57 5.2 Exterior Derivative 62 5.3 Stokes's Theorem 65 viii Contents 5.4 Vector Integral Theorems 67 6 Over a Map 71 6.1 Vector Fields Over a Map 71 6.2 One-Form Fields Over a Map 73 6.3 Basis Fields Over a Map 74 6.4 Fullbacks and Pushforwards 76 7 Directional Derivatives 83 7.1 Lie Derivative 85 7.2 Covariant Derivative 93 7.3 Parallel Transport 104 7.4 Geodesic Motion 111 8 Curvature 115 8.1 ExpLIcit Transport 116 8.2 Torsion 124 8.3 Geodesic Deviation 125 8.4 Bianchi Identities 129 9 Metrics 133 9.1 Metric Compatibility 135 9.2 Metrics and Lagrange Equations 137 9.3 General Relativity 144 10 Hodge Star and Electrodynamics 153 10.1 The Wave Equation 159 10.2 Electrodynamics 160 11 Special Relativity 167 11.1 Lorentz Transformations 172 11.2 Special Relativity Frames 179
942			_cWB16