关于柱函数的教学探讨

Discussion on Cylindrical Function Teaching

柱函数是数学物理方法中的一个重要内容,它包括贝赛尔函数、诺伊曼函数和汉克尔函数。这些函数表达复杂、性质众多、计算过程繁琐,学生在学习过程中感到很困惑。特别是柱函数积分计算比微积分中的积分要困难得多,通常使用洛梅尔积分教学计算。它的特点是只涉及同类柱函数乘积的积分。而在同轴谐振腔和同轴波导教学中,我们经常要涉及不同种类柱函数乘积的积分。因此,对这类积分进行研究,得到一般公式并应用于教学。

Cylindrical function is an important content of methods of mathematical physics. It includes Bessel function, Neumann function and Hankel function. Since these functions have complex expressions, lot of properties and the complicated process of calculation, students feel difficult to master them. In particular, the integral of cylindrical function by Lomel integral is more difficult than it in higher mathematics, which is usually the integral of same kind cylindrical function. However, the integral of different kind cylindrical function will appears in the teaching process of coaxial resonator and coaxial waveguide. Hence, this integral will be studied in teaching process.