摘要
δ函数是人为定义出来的一种分析工具,正因为它在数学上的简单性,才导致了它在物理上被广泛应用于研究质量、能量在空间或时间上高度集中的各种物理现象.它没有通常意义下的“函数值”,但是,当δ函数被当作普通函数参加运算,所得到的数学结论和物理结论是相互吻合的.本文在一维δ函数三种定义的基础上,讨论了多维δ函数的定义,以及多维δ函数的筛选性质、函数分解乘积性质、奇偶性、数乘性质和方差性质.并推广了多维δ函数的三个物理应用.
Delta function is a deliberately defined mathematical tool for analysis,which is devoted particularly to illustrating of the physical model of points distribution, and which is widely applied to analyze the high concentration of quality and energy on one point in space or in time in physics. It does not share ＂function value＂ in a general sense. However, when it is used as ordinary function for calculation, it makes mathematical conclusions,which correspond to physical ones. Based on three definitions of a dimensional δ function, the definition of multi-dimensional, its screening nature, function decomposition product nature,odevity,the number rides the nature and the variance have been discusses in the present proofed. Its three physical applications have been proofed and illustrated.
出处
《西安工业学院学报》
2006年第2期175-178,共4页
Journal of Xi'an Institute of Technology
关键词
多维δ函数
瞬时脉冲
点分布模型
狄拉克函数
函数性质
multi-dimensional δ function
instantaneous pulse
selects the distributed model
dirac function
function nature.
