第一型曲线积分在求柱体侧面积中的应用

针对学生在应用二重积分求柱体侧面积中所遇到的实际困难,指出了第一型曲线积分的几何意义,并通过四道例题给出了第一型曲线积分在求柱体的侧面积时的应用.

用微元法求旋转体侧面积的一个注记

证明了当Δx→0时,ΔS-2πf(x)dx不是比Δx高阶的无穷小,而ΔS-2πf(x)1+(f(′x))2dx是比Δx高阶的无穷小.

Schwarz不等式及旋转体侧面积的计算问题

文章应用Schwarz不等式的知识,给出了旋转体侧面积计算公式的一个新颖的证明,并同时指出用定积分计算旋转体侧面积时应该避免发生的错误。

四循三学:基于循证的精准教学——以六年级“圆柱的侧面积”学习为例

循证教学是指凭借证据实施教学,能弥补传统的依据个体经验进行教学实践的偏失。以“圆柱的侧面积”学习为例,介绍对循证教学中的“四循三学”(循证准备、循证过程、循证教学、诊测循证;前置学习、课堂学习、矫正学习)的思考与教学实践。

Influence of aluminum content on machinability of AS series cast magnesium alloys

The influence of Al content on machinability of AS series cast Mg alloys was studied. The assessment of machinability of Mg alloys was performed by measuring the cutting forces and surface roughness. The microstructure and the tensile properties were also studied. The results reveal that cutting forces are increased with the increase of the Al content. Surface roughness and mechanical properties are the highest for AS91 Mg alloy. It is assumed that the main mechanism, which has an influence on the mechanical properties, is the presence of intermetallic phases(Mg2Si and Mg17Al12). Cutting forces increase with the increase of the cutting speed in machining of all Mg alloys. These measured data are in accordance with the mechanical properties of the machined alloys.