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“数学物理方法”可视化素材资源库建设及教学实践

Development and Teaching Practice of a Visualization Resource Library for “Methods of Mathematical Physics”

Education Study / 2025,7(4): 488-491 / 2025-04-30 10 9

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• Authors: 黄海深      吴波     
• Information:

  遵义师范学院物理与电子科学学院，遵义

• Keywords: Wave equation; Finite difference method; Visualization; Numerical solution 波动方程；有限差分法；可视化；数值解
• Abstract: As a compulsory course for physics majors, “Mathematical Physics Methods” poses significant challenges for students in forming clear physical imagery under traditional teaching approaches due to its abstract content and complex mathematical derivations. Addressing the insufficient exploration of complex function theory in existing research and the overreliance on commercial software, this paper proposes constructing a visualization resource library covering complex function theory, mathematical physics equations, and special function theory using C++ programming. By employing methods such as finite difference schemes and interpolation algorithms, coupled with the free software Gnuplot for graphical rendering, we achieve intuitive representations of mathematical tools applied to physical problems. Taking the one-dimensional wave equation as an example, dynamic simulations visually demonstrate waveform evolution over time. Teaching practices demonstrate that this resource library effectively enhances students’ theoretical comprehension and classroom engagement. “数学物理方法”作为物理学专业的必修课程，因其内容抽象、数学推导复杂，在传统教学模式下，学生难以建立清晰的物理图像。针对现有研究中复变函数论探索不足且过度依赖商业软件等问题，本文提出以C++编程为工具，构建覆盖复变函数论、数学物理方程和特殊函数论的可视化素材资源库。通过运用有限差分法、插值算法等方法，并借助免费的Gnuplot生成图像，实现数学工具对物理问题的直观表达。以一维波动方程为例，动态展示波形随时间的演化。教学实践表明，该资源库的使用能够提升学生的理论理解能力与课堂参与度。
• DOI: https://doi.org/10.35534/es.0704094
• Cite: 黄海深，吴波．“数学物理方法”可视化素材资源库建设及教学实践［J］．教育研讨，2025，7（4）：488-491．