TO -<br > ix<br > ~hen you begin to study calculus， you will find that you have enconn-<br > tered many of its concepts and techniques before. Calculus makes extensive<br > use of plane geometry and algebra， two branches of mathematics with which<br > you are already familiar. However， added to these is a third ingredient，<br > which may be new to you: the notion of limit and of limiting processes.<br > From the idea of limit arise tile two principal concepts that form tile<br > nucleus of calculus; these are the derivative and the integral.<br > Tile derivative can be thought of as a rate of change， and this interpreta-<br > tion has many applications. For example， we may use tile derivative to<br > find the velocity of an object， such as a rocket， or to determine tbe<br > maximum and minimum values of a function. In fact， the derivative provides<br > so much information about the behavior of functions that it greatly simplifies<br > graphing them. Because of its broad applicability， tile derivative is as<br > important in such disciplines as physics， engineering， economics， and<br > biology as it is in pure mathematics.<br > The definition of tile integral is motivated by the familiar notion of area.<br > Although the methods of plane geometry enable us to calculate tile areas<br > of polygons， they do not provide ways of finding the areas of plane regions<br > whose boundaries are curves other than circles. By means of the integral<br > we can find the areas of many such regions. We will also use it to<br > calculate volumes， centers of gravity， lengths of curves， work， and hydro-<br > static force.<br > The derivative and the integral have found many diverse uses. The<br > following list， taken from the examples and exercises in tiffs book， illustrates<br > tile variety of the fields in which these powerful concepts are employed.<br >