学生在电动力学中的向量微积分困难
Students' difficulties with vector calculus in electrodynamics
摘要：
理解微分形式的麦克斯韦方程组在研究高级电磁学课程中讨论的电动力学现象时非常重要。因此，有必要让学生掌握向量微积分在物理环境中的应用。在这方面，我们调查的困难，二年级学生在鲁汶遇到的分歧和卷曲的向量场在数学和物理方面。我们发现，他们在计算方面相当熟练，但在解释向量场的图形表示和将向量微积分应用于物理情况方面很困难。我们已经发现了强烈的迹象表明，传统的教学是不够的，我们的学生充分理解的意义和权力麦克斯韦方程组在电动力学。
英文摘要：
Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.
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