The Differentiable Functions from R into Rn

Abstract

Summary.In control engineering, differentiable partial functions from R into R n play a very important role. In this article, we formalized basic properties of such functions.MML identifier: NDIFF 4, version: 7.1 .0 4.1 .11The notation and terminology used in this paper are introduced in the following articles: [25

Differential Equations on Functions from R into Real Banach Space

“…As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations on real Banach space.…”