Calculus with analytic geometry

Calculus with analytic geometry pdf epub mobi txt 电子书 下载 2025

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价格:90.00
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isbn号码:9780155057289
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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 >

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