微积分(英文影印版.原书第9版)

    书籍
    数学书籍
这是一本在美国大学中使用面比较广泛的微积分教材，有重视应用、便于自学、习题数量与内容比较丰富等特点。而与其他美国教材的差别在于严谨性，本书许多定理都有较严谨的证明，这一点与我国许多现行的理工科微积分教材比较类似，在美国也是另一种风格的教材。.
本书强调应用，习题数量多，类型多，重视不同数学学科之间的交叉，强调其实际背景，反映当代科技发展。每章之后有附加内容，有利用图形计算器或数学软件计算的习题或带研究性的小题目等。...

出版说明.
序
Preface
0 Preliminaries
0.1 Real Numbers, Estimation, and Logic
0.2 Inequalities and Absolute Values
0.3 The Rectangular Coordinate System
0.4 Graphs of Equations
0.5 Functions and Their Graphs
0.6 Operations on Functions
0.7 Trigonometric Functions
0.8 Chapter Review
Review and Preview Problems
1 Limits
1.1 Introduction to Limits
1.2 Rigorous Study of Limits
1.3 Limit Theorems
1.4 Limits Involving Trigonometric Functions
1.5 Limits at Infinity; Infinite Limits
1.6 Continuity of Functions

　　The ninth edition of Calculus is again a modest revision. Some topics have been added, and some of the topics have been rearranged, but the spirit of the book has remained unchanged. Users of previous editions have reported success, and we have no intention of overhauling a workable text. .
　　To many, this book would still be considered a traditional text. Most theorems are proved, left as an exercise, or left unproved when the proof is too difficult. When a proof is difficult, we try to give an intuitive explanation to make the result plausible before going on to the next topic. In some cases, we give a sketch of a proof, in which case we explain why it is a sketch and not a rigorous proof. The focus is still on understanding the concepts of calculus. While some see the emphasis on clear, rigorous presentation as being a distraction to understanding calculus, we see the two as complementary. Students are more likely to grasp the concepts of calculus if terms are clearly defined and theorems are clearly stated and proved.
　　A Brief Text The ninth edition continues to be the briefest of all the successful mainstream calculus texts. We have tried to prevent the text from ballooning upward with new topics and alternative approaches. In less than 800 pages, we cover the major topics of calculus, including a preliminary chapter, and the material from limits to vector calculus. In the last few decades, students have developed some bad habits. They prefer not to read the textbook. They want to find the appropriate worked-out example so it can be matched to their homework problem. Our goal with this text continues to be to keep calculus as a course focused on some few basic ideas centered around words, formulas, and graphs. Solving problem sets, while crucial to developing mathematical and problem-solving skills, should not overshadow the goal of understanding calculus.
　　Concepts Review' Problems To encourage students to read the textbook with understanding, we begin every problem set with four fill-in-the-blank items. These test the mastery of the basic vocabulary, understanding of theorems, and ability to apply the concepts in the simplest settings. Students should respond to these items before proceeding to the later problems. We encourage this by giving immediate feedback; the correct answers are given at the end of the problem set. These items also make good quiz questions to see whether students have done the required reading and have prepared for class.
　　Review and Preview Problems We have also included a set of Review and Preview Problems between the end of one chapter and the beginning of the next. Many of these problems force students to review past topics before starting the new chapter. For example,
　　Chapter 3, Applications of Derivatives: Students are asked to solve inequalities like the ones that arise when we ask where a function is increasing/decreasing or concave up/down.
　　Chapter 7,Techniques of Integration: Students are asked to evaluate a number of integrals involving the method of substitution, the only substantive technique they have learned up to this point. Lacking skill using this technique would spell disaster in Chapter 7.
　　Chapter 13, Multiple Integration: Students are asked to sketch the graphs of equations in Cartesian, cylindrical, and spherical coordinates. Visualizing regions in two- and three-space is key to understanding multiple integration.
　　Other Review and Preview Problems ask the student to use what they already know to get a head start on the upcoming chapter. For example,
　　Chapter 5, Applications of Integration: Students are asked to find the length of a line segment between two functions, exactly the skill required to perform the slice, approximate, and integrate in the chapter. Also, students are asked to find the volume of a small disk, washer, and shell. Having worked these out before beginning the chapter would make the students better prepared to understand the idea of slice, approximate, and integrate as it applies to finding volumes of solids of revolution.
　　Chapter 8, Indeterminate Forms and Improver Integrals: Students are asked to find the value of an integral like for a = 1, 2, 4, 8, 16. We hope that students will work a problem like this and realize that as a grows, the value of the integral gets close to 1, thereby setting up the idea of improper integrals. There are similar problems involving sums before the chapter on infinite series.
　　Number Sense Number sense continues to play an important role in the book. All calculus students make numerical mistakes in solving problems, but the ones with the number sense recognize an absurd answer and rework the problem. To encourage and develop this important ability, we have emphasized the estimation process. We suggest how to make mental estimates and how to arrive at ballpark numerical answers. We have increased our own use of this in the text, using the symbol where we make a ballpark estimate. We hope students do the same, especially in problems with the mark.
　　The Technology Projects that were at the end of the chapters in the eighth edition are now available on the Web in pdf files.
　　Changes in tile Ninth Edition The basic structure, and the overriding spirit, of the text has remained unchanged. Here are the most significant changes in the ninth edition:
　　There is a set of Review and Preview Problems between the end of one chapter and the beginning of the next.
　　The preliminary chapter, now called Chapter 0, has been condensed. The "precalculus" topics (that were in the beginning of Chapter 2 of the eighth edition) are now placed in Chapter 0. In the ninth edition, Chapter 1 begins with limits. How much of Chapter 0 needs to be covered depends on the background of the students and will vary from institution to institution.
　　The sections on antiderivatives and an introduction to differential equations have been moved to Chapter 3. This allows a clear break between "rate of change" concepts and "accumulation" concepts, because Chapter 4 now begins with area, followed immediately by the definite integral and the fundamental theorems of calculus. "It has been the author's experience that many first-year students of calculus fail to make a clear distinction between the very different concepts of the indefinite integral (or antiderivative) and the definite integral as the limit of a sum." That was from the first edition, published in 1965, and it is just as true today. We hope that separating these topics will draw attention to the distinction.
　　Probability and fluid pressure have been added to the Chapter 5, Applications of Integration. We emphasize that probability problems are treated much like mass problems along a line. The center of mass is the integral of x times the density, and the expectation in probability is the integral of x times the (probability) density. ..
　　Material on conic sections has been condensed from five sections into three sections. Students have seen much (but not all) of this material in their precalculus courses.
　　Vectors have been consolidated into a single chapter. In the eighth edition, we covered plane vectors in Chapter 13 and space vectors in Chapter 14. With this approach, we ended up repeating a number of topics, such as the dot product and curvature, in Chapter 14. The approach in the ninth edition is to cover vectors once. Most of the presentation is in terms of vectors in space, but we point out how plane vectors work. The context of a problem should dictate whether plane vectors or space vectors are needed.