由两例不定积分考研题引发的延伸探究  

Exploration of Two Questions About Indefinite Integral in Unified National Graduate Entrance Examination

作　　者：王成强 赵向青 吕志伟 李红玲[1] WANG Cheng-qiang;ZHAO Xiang-qing;LV Zhi-wei;LI Hong-ling(School of Arts and Sciences,Suqian University,Suqian 223800,China)

机构地区：[1]宿迁学院文理学院,江苏宿迁223800

出　　处：《广州城市职业学院学报》2023年第1期41-44,80,共5页Journal Of Guangzhou City Polytechnic

基　　金：国家自然科学基金项目“几类色散波方程能稳问题的统一处理”(编号:11701050);宿迁学院人才引进项目“控制系统的镇定与同步问题的研究”(编号:2022XRC033);宿迁学院“西楚学者”培养计划项目。

摘　　要：不定积分是诸如数学分析、微积分等大学数学类课程的教学重难点。将两道全国硕士研究生招生考试中的不定积分问题和已学的课程知识连接,并将他们形成知识小模块,顺应试题蕴含的关于不定积分的教学改革的最新发展趋势,将其作进一步延伸推广,以期能缓解不定积分知识模块的教学难度,能恰当凸出不定积分知识模块在大学数学类课程中的重要程度,能引导学生相对系统掌握零散的不定积分知识与技能。Indefinite integral is an important and difficult point in the teaching of college mathematics courses like mathematical analysis and calculus.Two questions about indefinite integral in Unified National Graduate Entrance Examination are connected with what students have learned,and formed into knowledge modules to comply with the latest development trend of teaching reform of indefinite integrals.The aim is to ease the difficulty of teaching indefinite integrals,to highlight the importance of indefinite integrals in college mathematics courses,and to guide students to acquire systematic knowledge and skills of indefinite integral.

关 键 词：考研数学 不定积分 凑微分法 待定系数法 

分 类 号：O172[理学—数学]