袖珍电子书挑战百度早知道

老翁认为，微积分是什么？“百度知道”栏目是在胡说八道，误人子弟。

痴迷百度知道的青年学子确实可怜又可悲。对于微积分是什么？袖珍电子书的回答是：微积分是研究事物变化的数学理论。根据何在？

世界知名数理逻辑大家G.Keisler在“基础微积分”教材的引言中的最后一句话是：“we present a large number of example, and we develop the mathematical theory with great care（极为细心地）.”

这句话的意思是，微积分是关于事物变化的数学理论。现将基础微积分的引言全文转载如下，请读者仔细研读参考：

基础微积分引言(此文于2013年7月11日上传放飞互联网) ，全文如下：

INTRODUCTION

      While arithmetic deals with sums, differences, products, and quotients, calculus deals with derivatives and integrals. The derivative and integral can be described in everyday language in terms of an automobile trip. An automobile instrument panel has a speedometer marked off in miles per hour with a needle indicating the speed. The instrument panel also has an odometer which tallies up the distance travelled in miles (the mileage). 

       Both the speedometer reading and the odometer reading change with time; that is, they are both “functions of time,” The speed shown on the speedometer is the rate of change, or derivative, of the distance. Speed is found by taking a very small interval of time and forming the ratio of the change in distance to the change in time. The distance shown on the odometer is the integral of the speed from time zero to the present. Distance is found by adding up the distance travelled from the first use of the car to the present. 

        The calculus has a great variety of applications in the natural and social sciences. Some of the possibilities are illustrated in the problems. However, future applications are hard to predict, and so the student should be able to apply the calculus himself in new situations. For this reason it is important to learn why the calculus works as well as what it can do. To explain why the calculus works, we present a large number of example, and we develop the mathematical theory with great care.

    说明：数学理论公理化，何须非非议？