数学分析中的非蕴含关系

Non-implicational relations in mathematical analysis

总结了数学分析中的一些非蕴含关系,极值点与稳定点的关系;(x0,f(x0))是y=f(x)的拐点与f(x0)=0的关系;不定积分与定积分存在性的关系;integral from n=α to +β f(x)dx收敛与limx→+βf(x)=0的关系;二重极限与累次极限存在性的关系;二元函数连续与偏导数存在性的关系;二重积分与二次积分存在性的关系.研究这些关系有助于更好地理解数学分析中的一些概念.

Summarized some non-implicational relations in mathematical analysis.These relations are as follows：the relation between the extreme point and the stable point,the relation between（x0,f（x0）） being the inflexion of y f（x） and f（x0）=0,the relation between the existence of indefinite integral and definite integral,the relation between the convergence of a integral from n=α to ＋β f（x）dx and limx→＋βf（x）=0,the relation between the existence of double limit and repeated limit,the relation between the continuousness of dual function and the existence of partial derivative,the relation between the existence of double integral and repeated integral.Studying these relations is convenient for us to make some concepts in mathematical analysis better understood.