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This is more of a extended comment than answer. I like to think every kind of derivative as boundary maps of some chain complex. Given a The tutorials present specialized applications of the DifferentialGeometry package. . ExteriorDerivative: take the exterior derivative of a differential form. The module will then look at calculus on manifolds including the study of vector fields, tensor fields and the Lie derivative. The module will then go on to study6 Aug 2018 Preface. These are notes for the lecture course “Differential Geometry I” given by the . 5.2.2 Covariant Derivative of a Global Vector Field . Vector derivative and the fundamental theorem of calculus. • Differentials and codifferentials for mappings and fields. • Coordinate-free differential geometry. 28 Jun 2015 3 Jun 2015 many excellent texts in Differential Geometry but very few have an early introduction to differential 4.4.2 Covariant Derivative Formulation of Curvature . 3 May 2004 differential geometry of curves and surfaces Kreyszig book [14] has also been taken as a .. Special case: Lie derivative of the metric . Basics of Euclidean Geometry, Cauchy-Schwarz inequality. The covariant derivative and Lie bracket; Riemann curvature tensor and Gauss's formulas