空间曲线的切线与法平面的求法及教学

On Solving and Teaching Tangent Line and Normal Plane of a Space Curve

为了克服死记公式的缺陷,提高解题灵活性,从而帮助学生更好掌握多元函数微分学的几何应用,针对以一般式方程表示的空间曲线求其上某点处切线与法平面方程的问题,设计出三种解决方案.实例分析显示所提求解方法可行,并由此建议更改"曲面上某点处的法线和切平面"和"曲线上某点处的切线和法平面"两部分内容的教学次序.

The purpose of this paper is to improve the problem-solving flexibility ,and to help better grasping geometric applications of differential calculus of multivariate functions .For a point on a space curve of the general equation ,three approaches to the equation of tangent line or normal plane are provided .An example is shown that these approaches are feasible .The author suggests an order switch in teaching “normal line and tangent plane of a space curve” and“tangent line and normal plane of a space curve” .