A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
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热方程的三重方法：数据、建模、数值
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
James G. Puckett
中科院分区：
文献类型：
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作者：
K. Spayd;James G. Puckett
摘要本文介绍了在一学期的本科偏微分方程课程中，我们对一维热（扩散）方程的建模教学方法。我们建造了一个装置来演示热扩散通过一个又长又细的金属棒，每一端都有规定的温度。学生们观察了物理现象，收集了沿杆的温度数据，然后在课堂内外参考了演示。在这里，我们讨论了实验设置，演示如何影响课堂实践和基于收集数据的项目，包括分析和计算组件。
Abstract This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components.