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

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.