Tangent Space and Derivative Mapping on Time Scale

A pseudo-Euclidean space, or Smarandache space is a pair (Rn, ω|− → O ). In this paper, considering the time scale concept on Smarandache space with ω|− → O (u) = 0 for ∀u ∈ E, i.e., the Euclidean space, we introduce the tangent vector and some properties according to directional derivative, the delta differentiable vector fields on regular curve parameterized by time scales and the Jacobian matrix of -completely delta differentiable two variables function.