Algebraic Differential Calculus

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Preliminary version, last change. March, 2002. In the original *.ps files there are no pages 110-112, 152. It's ok. Title: Algebraic Differential Calculus Contents Chapter I. Kaehler Differentials 1_1 Derivations Tangent Spaces and Vector Fields 1_2 The Module of Kaehler Differentials Tangent Bundles 1_3 Differential Modules of Field Extensions 1_4 Differential Modules of Local Rings 1_5 Differential Modules of Affine Algebras and their Localizations 1_6 Smooth Algebras 1_7 Differential Modules of Complete Intersections 1_8 Existence of Universally Finite Derivations 1_9 The Kaehler Differents (Jacobian Ideals) of an Algebra Introduction to the bibliography I Chapter I I. Differential Operators 2_1 Basic Properties of Differential Operators 2_2 Universal Differential Operators 2_3 Functorial Properties 2_4 Differential Operators of Smooth Algebras Introduction to the bibliography I I Chapter I I I. Differential Forms 3_1 Differential Algebras 3_2 The Universal Differential Algebra. Universal Extension of Differential Algebras 3_3 Functorial Properties of the Universal Extension Introduction to the bibliography I I I Chapter IV. Connections 4_1 Connections on Modules 4_2 Curvature and Torsion of Connections 4_3 Riemannian Algebras 4_4 The Levi-Civita Connection 4_5 Curvature of Riemannian Algebras Solutions to some of the problems Appendices A Commutative Algebras B Dimension Formulas in Algebras of Finite Type. Quasifinite and Equidimensional Algebras C Complete Intersections D The Fitting Ideals of a Module Bibliography