数学专业英语2-5.ppt

1、New Words for the present we confine our attention to plane analytic geometry.,以后我们将更加详细地讨论三维笛卡儿几何学。目前将注意力集中于平面解析几何。,A geometric figure, such as a curve in the plane , is a collection of points satisfying one or more special conditions.,5-B Geometric figures,一个几何图形是满足一个或多个特殊条件的点集，比如平面上的曲线。,By transl

2、ating these conditions into expressions, involving the coordinates x and y, we obtain one or more equations which characterize the figure in question.,通过把这些条件转化成含有坐标x和y的表达式，我们就得到了一个或多个能刻画该图形特征的方程。,Throughout their historical development, calculus and analytic geometry have been intimately intertwine

3、d.,微积分与解析几何在它们的发展史上已经紧密地融合在一起了。,New discoveries in one subject led to improvements in the other. The development of calculus and analytic geometry in this book is similar to the historical development, in that the two subjects are treated together.,一门学科的新发现会导致另一门学科的进步。本书中所叙述的微积分和解析几何的发展和历史发展过程是相似的，因

4、为这两门学科是一起研究的。,However, our primary purpose is to discuss calculus. Concepts from analytic geometry that are required for this purpose will be discussed as needed.,不过，我们的主要目的是讨论微积分。为此，解析几何中的概念将只是在必要时讨论。,Actually, only a few very elementary concepts of plane analytic geometry are required to understan

5、d the rudiments of calculus.,实际上，仅仅在微积分入门阶段需要用到平面解析几何的几个基本概念。,A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and this study will be carried out using vector method.,如果想拓展微积分的范围与应用，需要进一步研究解析几何，而这种研究需用到向量的方法来实现。,Until then, all that is required from analytic geometry is a little familiarity with drawing graph