%0 Journal Article
%T 基于一题多解的数学分析思维拓展路径研究&#8212;&#8212;以第二型曲面积分的计算为例<br>Research on the Path of Expanding Mathematical Analysis Thinking Based on Multiple Solutions to a Single Problem&#8212;Taking the Calculation of the Second-Type Surface Integral as an Example
%A 张玉芳
%A 唐美燕
%A 吴小莉
%J Advances in Applied Mathematics
%P 88-93
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.146303
%X 本文采用案例分析法&#65292;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)&#65292;并构建了第二型曲面积分计算方法的决策树&#65292;给出了一题多解的教学启示。<br>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 &#8220;two-to-one&#8221; 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.
%K 一题多解&#65292
%K 数学分析&#65292
%K 思维拓展&#65292
%K 第二型曲面积分<br>Multiple Solutions to a Single Problem
%K Mathematical Analysis
%K Thinking Expansion
%K Second-Type Surface Integral
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=117406