Differential Geometry and Relativity Theories: tangent vectors, derivatives, paths, 1-forms
Differential Geometry and Relativity Theories: tangent vectors, derivatives, paths, 1-forms

Summary/Abstract: In this lecture note, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic to pics, for instance: (1) definition of tangent vectors; (2) change of coordinate system in the definition of tangent vectors; (3) action of tangent vectors on coordinate systems; (4) structure of tangent spaces.

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