多元函数极限教学的系统分析

A Systematic Analysis on the Teaching Method of the Limit of Multivariate Function

采用多元类比方法,对多元函数的概念、极限、分析性质与一元函数的相应内容进行比较,分析,揭示两者中的"形同实异"及"形异实同",按照系统论原则,从多元函数极限概念的内部结构与外部联系,从它的概念的形成与发展的来龙去脉加以认识,用系统化的方法做出全面的分析,对有效的理解和掌握多元函数极限及微分学起到重要作用。在此基础上给出求多元函数极限相应的教学策略。

The thesis compares with univariate function through the concept, limit, and analytic properties of multivariate function muhiple analogy method, it analyzes and reveals their differences as well as similarities. With a systematic and comprehensive analysis on the evolution, internal and external relations of multivariate function, this study is of great importance to effective understanding and teaching of multivariate function and differential calculus. This thesis also presents a teaching method for solving the limit of multivariate function.