Research on the Path of Expanding Mathematical Analysis Thinking Based on Multiple Solutions to a Single Problem—Taking the Calculation of the Second-Type Surface Integral as an Example
Year: 2025
Type: article
Abstract: 本文采用案例分析法，给出了一道经典第二型曲面积分的多种解法(如直接投影法、二化一法(合项法)、归一法、高斯公式法、参数方程法、轮换对称性法、物理意义法等)，并构建了第二型曲面积分计算方法的决策树，给出了一题多解的教学启示。This paper employs the case analysis method to present multiple approaches to solving a classic second-type surface integral (such as the direct projection method, the “two-to-one” method, the normalization method, the Gauss formula method, the parametric equation method, the rotational symmetry method, and the physical interpretation method). Based on these, a decision tree for calculating second-type surface integrals is constructed, along with pedagogical insights into the multi-solution approach to problem-solving.
Source: Advances in Applied Mathematics
Author: 玉芳 张
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411430935