高等数学教学中的两个难点解析  

Analysis on two teaching difficulties of advanced mathematics

作　　者：王凤鸣[1,2] 朱奇锋[1] 

机构地区：[1]河南财经学院成功学院,河南郑州451200 [2]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《南阳师范学院学报》2010年第3期91-93,共3页Journal of Nanyang Normal University

摘　　要：定积分概念是用极限定义的,有很强的思想性.按定积分概念,用计算定积分的方法求解无限和的极限或数列极限是教学中的一个难点,这里应对难点给出一个易掌握的处理方法.分部积分"分部"的意思是把两个函数u(x)和v(x)的乘积uv拆分为不定积分∫udv与∫vdu两部分的和,即uv=∫udv+∫vdu,其中∫eaxsinbxdx、∫sin(lnx)dx这一类的分部积分是教学中的又一个难点,处理这类不定积分方法的数学依据是这时的∫udv和∫vdu之间有一个容易得到的形如λ∫udv+μ∫vdu=w(x)(λ,μ为常数,λ≠μ)的线性关系.The concept of definite integral is defined by definition of limit, which is very ideological. According to the concept of definite integral, computing the limit of sum of infinite terms with techniques for computing deftnite integral is teaching difficulty. Here is a way that is easy to master. The word ＂parts＂ from integration by parts means to divide uv, the product of two functions u（x） and v（x）, into the sum of ∫udv and ∫vdu, that is uv =∫udv＋ ∫vdu. Computing infinite integral like ∫e^ax sinbxdx, ∫sin（lnx）dx is teaching difficulty. The basis of computing that kind of infinite integral is there is a obvious linear relationship like λ∫udv ＋μ∫vdu =w（x）（λ ,μ are constants,λ ≠μ） between ∫udv and ∫vdu.

关 键 词：定积分 极限 分部积分 难点 

分 类 号：O172.1[理学—数学] G420[理学—基础数学]