“电磁场与传输理论”中亥姆霍兹定理的类比教学法

亥姆霍兹定理是“电磁场与传输理论”中的一个重要定理，其数理表述抽象、物理意义深刻的特性使得学生在学习中普遍存在理解难度大的问题。我们通过优化教学方法，用类比教学法替代纯数学推导的传统教学方法，从电学谐振系统和力学的类比出发，可直观揭示亥姆霍兹定理所蕴含的数理意义。教学实践表明，通过类比教学法讲授亥姆霍兹定理具有很好的教学效果。

Analogous Methods in the Teaching of Helmholtz Theorem in Electromagnetic Field and Transmission Theory

In the teaching of electromagnetic field and transmission theory, Helmholtz theorem has brought great difficulty to students due to its abstract mathematical expression but profound physical meaning. To solve this problem, an optimized teaching method is introduced by replacing the conventional mathematical derivation with analogy. As is illustrated, the mathematical meaning of Helmholtz theorem can be intuitively revealed from the analogies of electrical and mechanical resonant systems. The optimized teaching method has been validated to be effective for clarifying the physical insights of Helmholtz theorem.