摘要
不定积分是高职数学中的教学重难点之一,求不定积分的常用方法包括换元积分法、换元积分法、分部积分法等。针对两道不定积分的例题,探索不定积分中两类问题的多种解法,涉及万能代换、待定系数积分法、无理代换、三角代换(割代换)、双曲代换、欧拉第一代换、欧拉第二代换等,比较了不同解法之间的联系与区别,分析各类解题技巧的特点,可以培养学生多元化的解题思路和多角度的思维方式,让学生学会一题多解、一题多变、一题多问,从而提高学生的发散思维能力和创新意识。
Indefinite integral is one of the key and difficult points in mathematics teaching in higher vocational colleges.Based on 2 examples of indefinite integral,various solutions are explored in this paper,involving universal substitution,integral method of undetermined coefficient,irrational substitution,trigonometric substitution,hyperbolic substitution,Euler first-generation substitution,Euler second-generation substitution and so on,and the connections and differences between different solutions are compared,and the characteristics of various solving skills are analyzed as well,so as to cultivate students’ability in problem solving in diversified and multi-angle ways.Therefore,students’divergent thinking and innovative consciousness can be improved by solving one with multiple solutions,various types and creative ideas.
作者
王雅萍
WANG Ya-ping(Jiangsu Vocational College of Commerce and Trade,Nantong 226001,China)
出处
《浙江水利水电学院学报》
2019年第5期87-90,共4页
Journal of Zhejiang University of Water Resources and Electric Power
关键词
高职数学
不定积分
一题多解
创新思维
mathematics teaching in higher vocational college
indefinite Integral
multiple solutions to one problem
innovative thinking
作者简介
王雅萍(1986-),女,江苏南通人,讲师,硕士,主要研究方向为应用数学。
