摘要
本文以非标准分析为工具,研究了核子上的积分与求导,并从实例出发,引出了Heaviside函数,又论证了Heaviside函数的导数就是Diracδ函数;从而给出了Diracδ函数一个精确的表示方法。之后又进一步研究了它的性质及应用。
In this paper the author has studied differentiation and integration on a
kernel with the nonstanard analysis as a tool, and introduced Heaviside-
function from practical examples, then proved that the derivative of Heaviside-
function is just the Dirac δ-function. Therefore, an accurate expression of
δ-function is obtained. Also, the properties and application of δ-function is
studied further in this paper.
关键词
像函数
Diracδ函数
核子
microcosmic analysis
open kernel
closed kernel
image function
Heaviside-function
Dirac δ-function
