医科院校定积分教学探析

The analysis on the teaching of definite integral in the medical universities

《微积分》中定积分概念的问题导入较为简化,与医科背景脱离,难以体现在医学中的应用价值.同时,用"无限细分求和"引出定积分,再推出牛顿-莱布尼茨公式的教法较为繁琐,学生不易理解积分与极限、微分的关系,加之耗费课时较多,压缩了应用性问题的教学内容,这与定积分教学目标相违背.为了确定积分的学习价值并保证学生在较少的课时内理解微分与积分等概念,教学中以"损伤面积的伤残鉴定"作为问题情境,以牛顿-莱布尼兹公式作为定积分定义,再反之推出和式的极限,进而解决实际问题,通过教学实践,取得了较好的教学效果.

In calculus, the conception of the definite integral was imported in a simpler way and from the medical background, not reflected in the application of medicine. At the same time, the traditional teaching that unlimited sub-sum leads the points, then introduce Newton-Leibniz formula may be too complex to make the students understand the relation among integral caculus, extreme limit and differential calculus, plus spend more hours, reduce the application of the actual question, this run counter to the goal of teaching. In order to determine the value of integration of learning and to ensure that students understanding differential and integral concepts in smaller classes, we based on question background of the wounded and disabled of the hurt area authenticating, defined the Newton-Leibniz formula as the definite integral concept and then deduced the extreme limit of the sum type, finally solved practical problems, through teaching practice, which has achieved good results teaching.