光滑曲线与可求长曲线的注记 |
| |
引用本文: | 付必胜,杨益民,沙峰.光滑曲线与可求长曲线的注记[J].大学数学,2011,27(6):140-142. |
| |
作者姓名: | 付必胜 杨益民 沙峰 |
| |
作者单位: | 1. 广东南海广播电视大学,南海,528200 2. 北京工商大学应用数学系,北京,100048 |
| |
摘 要: | 文献1]指出光滑性不是建立弧长计算公式的必要条件,并在导数x’(t),y’(t)可积的条件下建立了弧长计算公式.本文对可求长曲线弧长的计算问题进一步探讨,在黎曼(Riemann)可积条件下,给出有限维赋范线性空间上的曲线弧长计算公式.
|
关 键 词: | 可求长曲线 弧长 有限维赋范线性空间 内积空间 绝对连续函数 奇异函数 |
A Note on Smooth Curve and Rectifiable Curve |
| |
Abstract: | The paper 1] points out that smooth property is not the necessary condition of the calculation formula of arc length,and gives a calculation formula of arc length under the condition that derivativesx'(t),y'(t) are integrable. This paper further studies the calculating problem of arc length, and gives a calculation formula of arc length in the finite dimensional linear normed space under the condition that the curve is Riemann integrable. |
| |
Keywords: | rectifiable curve arc length finite dimensional linear normed space inner product space absolutely continuous function singular function |
本文献已被 万方数据 等数据库收录! |