空间解析几何在职工大学工科高等数学教材中属于多元微积分的基础部分,主要是为讲授多元微分学和多元积分学作准备的。因此在讲授本章时,应当十分重视本章与多元微积分特别是多元积分学的联系。在三重积分、曲面积分以及曲面面积的计算中,根据教学大纲的规定,常用的空间曲面为平面、球面、椭球面、旋转曲面(包括圆锥面)、椭圆抛物面以及二次柱面。学生在学习这些内容时大多不会有太大困难,难点在于画出空间曲面所围空间区域的草图和此空间区域在坐标平面上的投影,而这一部分特别是求空间区域在坐标平面上的投影却正是本章应完成的重点内容。如果我们在讲授这一部分内容时不够透彻或是忽视学生在这 Spatial Analytic Geometry belongs to the basic part of multivariate calculus in higher engineering math textbooks of workers’ universities, mainly for teaching multivariate calculus and multivariate integralism. Therefore, when teaching this chapter, we should attach great importance to this chapter and multivariate calculus, especially multivariate integralism. In the calculation of triple integral, surface integral and surface area, according to the syllabus, the commonly used space surface is plane, sphere, ellipsoid, rotating surface (including conical surface), elliptical parabola and quadratic cylinder. Most students will not have much difficulty learning these contents. The difficulty lies in drawing sketches of the space around the surface of the space and the projection of the space on the coordinate plane. In particular, this part is to find the space area on the coordinate plane Projection is precisely the focus of this chapter should be completed. If we are not teaching this part thoroughly or ignoring students here