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...Coursenotes tensor calculus and differential geometry wah lucflorack march cover illustration papyrus fragment from euclid s elements of book ii contents preface iii notation prerequisites linear algebra vector spaces bases dual thekroneckertensor inner products reciprocal mutual relations examples vectors covectors tensors in all generality subject to symmetries symmetryandantisymmetrypreserving product operators with an oriented volume on space transformations absolute i relative pseudo contractions thehodgestaroperator euclidean cartesian curvilinear coordinates differentiable manifolds tangent cotangent bundle exterior derivative afneconnection lie torsion levi civita connection geodesics curvature push forward pull back polar the plane a helicoidal extension...