数学专业多元微积分教学的几点体会

Some Observations on the Teaching of Multivariable Calculus for Math Major

介绍了在我校数学系二年级第一学期的本科生讲授多元微积分的一些做法.特别强调向量值函数的微分学和将实际问题转化为积分的微元分析法,且举例说明如何把学生已掌握的线性代数和常微分方程知识引入多元微积分中来,得到有重要意义的结果.

We present some strategy in our teaching of multivariable calculus for undergraduates majoring in mathematics.We emphasize differential calculus for vector valued functions and the method of infinitesimal element which is crucial for converting practical problems into integration.Moreover,we demonstrate how to get meaningful results by applying theory and technique from linear algebra and ordinary differential equations into multivariable calculus.