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前言 算子是爱尔兰数学家兼天文学家W.R.Hamilton建议采用的,所以也叫Hamilton算子。利用它可简化运算过程并使算式书写形式简练,因此在水利工程的技术计算和理论研究中经常用到。但由于是一个矢性微分算子,具有矢量和微分的双重性质,所以乍用起来,多不习惯,在运算时常感困难。因此,分析算子的运算特点,总结其运算规律就成为掌握算子这个数学工具,提高工程计算能力的重要一环。本文首先介绍算子的运算规则及其注意点,并通过典型算例说明运算规则的使用方法,以期对水利科技工作者掌握算子这一工程数学工具有所帮助。 由于笔者水平所限,文中不妥之处,记好者批评指正。
Preface The operator is proposed by W. R. Hamilton, an Irish mathematician and astronomer, so called Hamiltonian. Use it to simplify the calculation process and make formula writing concise, so in water conservancy engineering calculation and theoretical research is often used. However, due to the fact that it is a vector of differential operators, it has the dual nature of vectors and differentials. Therefore, it is often not used at first glance and often difficult in operation. Therefore, analyzing the operation characteristics of operators and summarizing their operation rules become an important part of mastering mathematical tools of operators and improving the engineering calculation ability. In this paper, we first introduce the operation rules of operators and their attention points, and explain the use of operation rules through typical examples in order to help operators of water conservancy science and technology grasp the mathematical tools of engineering. Due to the limited level of the author, the article inappropriate, remember good criticism correction.