初等函数求定义域方法的渐进式讲授  

Progressive Teaching Method of Finding Domain of Elementary Function

作　　者：解顺强[1] 

机构地区：[1]北京劳动保障职业学院,北京100029

出　　处：《北京劳动保障职业学院学报》2017年第4期54-58,共5页Journal of Beijing Vocational College Of Labour And Social Security

基　　金：北京市教委2013年教改项目;项目编号201306

摘　　要：求函数定义域是研究函数需要首先解决的问题,然而由于高职院校学生的数学基础普遍较差,且差异极大,这给微积分教学带来巨大挑战。于是提出初等函数定义域求法的讲授方法:首先,讲解不等式的解法,其中给出求解不等式的因式分解与符号表格方法;其次,讲解函数的加、减、乘、除运算对定义域的影响;第三,讲解复合运算对函数定义域的影响;第四,讲解其他基本初等函数的定义域;最后,从初等函数的构成出发,归纳出一般初等函数求定义域的步骤,并通过例题加以说明。Finding domain of function is the first problem to be solved for studying function.However,the mathematics foundation of students in higher vocational college is generally poor,and the difference is great,which brings great challenges to the teaching of calculus.This paper puts forward a teaching method of finding the domain of function which is different from the traditional method.First of all,the solution of inequality is explained,and the factorization and symbolic list method for solution of inequality is given here.Secondly,the influence of the addition,subtraction,multiplication and division of functions on the domain of function is given.Third,the influence of compound operation on domain of function is given.Fourth,the list gives the domains of other basic elementary functions.Finally,starting from the composition of elementary functions,we generalize the steps of finding the domain for general elementary functions,and illustrate them by examples.

关 键 词：微积分 函数 定义域 分层教学 

分 类 号：G623[文化科学—教育学]