基于函数■的高等数学教学探索

Teaching Exploration for Advanced Mathematics Based on the Function ■

主要基于高等数学中的重要函数sinx/x的教学作一些探讨.该函数在整个高等数学中扮演着极其重要的角色,它与重要极限、Jordan不等式、Dirichlet积分等有着紧密的联系.围绕该函数选取和设计了若干相关的教学实例,并对极限论、微分学、积分学、级数理论等模块中的重要知识点展开讨论,力争用一个函数将高等数学中的主要内容贯穿起来,展现知识体系的一脉相承性.实际教学中可利用启发式教学、探究式教学等多种手段,并结合数学软件讲深讲透这些案例,提高学生学习的兴趣和积极主动性,增强学生的创新思维能力,从而提高高等数学教学质量.

In this paper,an exploration has been made on the teaching methodology for advanced mathematics based on the important function sinx/x,which plays rather important role in the calculus,as it has close connections with the important limit,Jordan's inequality and Dirichlet integral.By choosing and designing some related examples for this function,the accompanied knowledge in the limit theory,differentiation theory,integration theory and infinite series theory has been explained.The using of one function to run through the main contents in advanced mathematics reveals the coherence property of the knowledge.In real teaching activities,we can use the methods of heuristic teaching,inquiry teaching and other means as well as some mathematical software to improve the interest and activity of learning and enhance the innovative thinking ability for students,and thus to improve the teaching quality for the course of higher mathematics.