《微积分》为海外**数学类教材系列丛书之一,从ThomsonLearning出版公司引进,本教材2003年全球发行约40余万册,在美国,占领了50%-80%的微积分教材市场,其用户包括耶鲁大学等**院校及众多一般院校600多所。
《微积分》历经多年教学实践检验,内容翔实,叙述准确、对每个重要专题,均用语言地、代数地、数值地、图像地予以陈述。作者及其助手花费了三年时间,在各种媒体中寻找了*能反映应用微积分的教学实例,并把它们编入了教材。因此,《微积分》例、习题贴近生活实际,能充分调动学生学习的兴趣,此外。《微积分》语言朴实、流畅.可读性强,比较适合非英语**的学生阅读。
值的一提的是,《微积分》较好地利用了科技。随书附赠两张CD-ROM,一张称为“感受微积分”,提供了一个实验环境,如同一个无声的老师,用探索、发现式的方法逐步���导学生分析并解决问题,还能链接到学习网站www.stewartcalculus.com。另一张称为“交直学习微积分”,包含有与微积分教学有关的视频与音频等。
《微积分》适于国内高等院校工科各专业和广大非数学专业(含文科、经管专业)本、专科生作为双语教学的教材使用。

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Preface xiv
To the Student xxvi
A Preview of Calculus 2
1 Functions and Hodels 10
1.1 Four Ways to Represent a Function 11
1.2 Mathematical Models: A Catalog of Essential Functions 25
i.3 New Functions from Old Functions 38
1.4 Graphing Calculators and Computers 48
1.5 Exponential Functions 55
1.6 Inverse Functions and Logarithms 63
Review 77
Principles of Problem Solving 80
2 Limils and Derivatives 8G
2.1 The Tangent and Velocity Problems 87
2.2 The Limit of a Function 92
2.3 Calculating Limits Using the Limit Laws 104
2.4 The Precise Definition of a Limit 114
2.5 Continuity 124
2.6 Limits at Infinity; Horizontal Asymptotes 135
2.7 Tangents, Velocities, and Other Rates of Change 149
2.8 Derivatives 158
Writing Project o Early Methods for Finding Tangents 164
2.9 The Derivative as a Function 165
Review 176
Problems Plus 180
3 Lifferenliatiun Rules 182
3.1 Derivatives of Polynomials and Exponential Functions 183
3.2 The Product and Quotient Rules 192
3.3 Rates of Change in the Natural and Social Sciences 199
3.4 Derivatives of Trigonometric Functions 211
3.5 The Chain Rule 217
3.6 Implicit Differentiation 227
3.7 Higher Derivatives 236
Applied Project o Where Should a Pilot Start Descent? 243
Applied Project o Building a Better Roller Coaster 243
3.8 Derivatives of Logarithmic Functions 244
3.9 Hyperbolic Functions 250
3.10 Related Rates 256
3.11 Linear Approximations and Differentials 262
Laboratory Project o Taylor Polynomials 269
Review 270
Problems Plus 274
4 Applications of gifferenliulion 278
4.1 Maximum and Minimum Values 279
Applied Project o The Calculus of Rainbows 288
4.2 The Mean Value Theorem 290
4.3 How Derivatives Affect the Shape of a Graph 296
4.4 Indeterminate Forms and L'Hospital's Rule 307
Writing Project o The Origins of L'Hospitars Rule 315
4.5 Summary of Curve Sketching 316
4.6 Graphing with Calculus and Calculators 324
4.7 Optimization Problems 331
Applied Project o The Shape of a Can 341
4.8 Applications to Business and Economics 342
4.9 Newton's Method 347
4.10 Antiderivatives 353
Review 361
Problems Plus 365
5 Inteorals 360
5.1 Areas and Distances 369
5.2 The Definite Integral 380
Discovery Project o Area Functions 393
5.3 The Fundamental Theorem of Calculus 394
5.4 Indefinite Integrals and the Net Change Theorem 405
Writing Project o Newton, keibniz, and the Invention of Calculus 413
5.5 The Substitution Rule 414
5.6 The Logarithm Defined as an Integral 422
Review 430
Problems Plus 434
6 Applicotions of Inteoration 436
6.1 Areas between Curves 437
6.2 Volumes 444
6.3 Volumes by Cylindrical Shells 455
6.4 Work 460
6.5 Average Value of a Function 464
Applied Project o Where to Sit at the Movies 468
Review 468
Problems Plus 470
7 Techniques of Integration 474
7.1 Integration by Parts 475
7.2 Trigonometric Integrals 482
7.3 Trigonometric Substitution 489
7.4 Integration of Rational Functions by Partial Fractions 496
7.5 Strategy for Integration 505
7.6 Integration Using Tables and Computer Algebra Systems 511
Discovery Project o Patterns in Integrals 517
7.7 Approximate Integration 518
7.8 Improper Integrals 530
Review 540
Problems Plus 543
8 Further Applications of Inteoralion 546
8.1 Arc Length 547
Discovery Project o Arc Length Contest 554
8.2 Area of a Surface of Revolution 554
Discovery Project o Rotating on a Slant 560
8.3 Applications to Physics and Engineering 561
8.4 Applications to Economics and Biology 571
8.5 Probability 575
Review 582
Problems Plus 584
9 Diffeiential Equations 586
9.1 Modeling with Differential Equations 587
9.2 Direction Fields and Euler's Method 592
9.3 Separable Equations 601
Applied Project How Fast Does a Tank Drain? 609
Applied Project Which Is Faster, Going Up or Coming Down? 610
9.4 Exponential Growth and Decay 611
Applied Project Calculus and Baseball 622
……
10 Parametric Equations and Polar Coordinates
11 Infinite Sequences and Series
12 Vectors and the Geometru of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
17 Second-Order Offerential Equations
Appendixes
Index
……