热传导方程初边值问题的可视化教学——《数学物理方程》的教学实践
Visualization Teaching of the Heat Equation with Initial-Boundary Conditions—Teaching Practice of The Equation of Mathematical Physics

《数学物理方程》的可视化教学有助于激发学生的学习热情、提高教学效果。本文通过数学软件Matlab求解具有三类典型边界条件的热传导方程初边值问题，通过绘制方程的解在不同时间下的函数图像，直观地展示了三类边界条件如何影响方程的解，加深了学生对抽象的初边值问题的理解，培养了学生的直觉思维能力和观察能力。
The visual teaching of The Equation of Mathematical Physics helps stimulate students’ enthusiasm for learning and improve the teaching effect. This paper uses mathematical software Matlab to solve the heat equation with initial and three typical boundary conditions. By drawing function images of the equation’s solutions at different times, we intuitively demonstrate how the three types of boundary conditions affect the solutions of the equation, which deepens students’ understanding of the abstract initial-boundary value problems, and cultivates their intuitive thinking ability and observation ability.