利用直角坐标计算二重积分的教学设计

Teaching Design for Calculating Double Integral Using Cartesian Coordinates

二重积分是高等数学的一个重要组成部分,在一元函数定积分向多元函数重积分的转化中起着至关重要的作用。二重积分以一元函数定积分为基础,但是难度却大大增加。本文提出了探究式课堂教学设计,通过创设情景提出问题、引导讨论解决问题、概括归纳得出结论、巩固练习深化理解和课堂小结引申探究等教学模块来充分调动学生的主观能动性,使学生深刻理解并熟练掌握直角坐标系下把二重积分转化为二次积分的计算方法。

Double integral is an important part of higher mathematics. It plays a crucial role in the transformation of integrals from one function to multiple integrals. The double integral is based on the integral of a one-variable function, but the difficulty is greatly increased. This paper proposes an inquiry-based classroom instructional design. Through creating scenarios, asking questions, guiding discussions and solving problems, summarizing and summing up conclusions, consolidating exercises and deepening comprehension, and summarizing and summarizing the lessons in class to fully mobilize students＇ subjective initiative, the students will have a deeper understanding and mastering the calculation method of converting double integrals into quadratic integrals in rectangular coordinates.