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中国数学会上海分会中学数学研究委员会编,“数列与极限”一书的特点: (一)直观性强,正如本书序言里所说的:本册在讲法上结合图象,力求直观,………。本书的确是完成了这一目的,并且完成得很好。如数列的图象表示法,一方面用坐标平面上的点来表示,便于观察数列的性质,另一方面又用数轴上的点来表示,则便于研究数列的极限。 (二)每一个概念的提出,都是从具体的例子很自然地诱导出来的。概念的形成,大有“犹水之就下,孰能御之”之势。这在无穷大量,无穷小量,极限各节显得特别突出。
The mathematics of the Shanghai Branch of the Chinese Mathematical Society Secondary School Mathematics Research Committee, “Numbers and Limits” book features: (A) intuitive and strong, as the book said in the preface: This book combines images in lectures, strive to be intuitive,... .... This book does accomplish this goal and it is done very well. For example, the image representation of a series of numbers is represented by points on the coordinate plane on the one hand, which is convenient for observing the nature of the series, and on the other hand, it is represented by points on the number axis, so that it is convenient to study the limit of the series. (b) The formulation of each concept is naturally induced by concrete examples. The formation of the concept has a great tendency of “Jiu Shui is the next, and the ability to defend it”. This is extremely large, infinitely small, and the extreme sections are particularly prominent.