摘要
二重积分理论是诸如数学分析等课程中的最重要的知识模块之一。文章以2009年全国大学生数学竞赛非数学专业组预赛中的二重积分计算题为例,探讨了二重积分的一题多解问题,提出了在教学中要重视应用定义法、截线积分法、Green公式计算法,以及换元积分法来计算二重积分。
Double integral theory is one of the most important modules in college mathematics courses such as Mathematical Analysis.On the basis of the query to calculate a double integral in the first question of the preliminary contest paper for non-mathematics majors of the first College Mathematics Contest of China(held in 2009),the teaching of finding multi-solutions to double integral problems is discussed and it is obtained that the teaching of finding multi-solutions to double integral problems should attach importance to the teaching of calculating double integrals by the definition method,integrating by using slice lines,Green's formula and integration by change of variables.
作者
王成强
WANG Chengqiang(School of Mathematics, Chengdu Normal University, Chengdu 611130, China)
出处
《成都师范学院学报》
2020年第3期105-113,共9页
Journal of Chengdu Normal University
基金
国家自然科学基金青年基金“几类色散波方程能稳问题的统一处理”(11701050)。
关键词
大学数学竞赛
二重积分
“截线”积分法
Green公式法
换元积分法
college mathematics contest
double integrals
method of integrating by slice lines
method of integrating by Green's formula
integration by change of variables
