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微积分 第7版 上 影印版PDF|Epub|txt|kindle电子书版本网盘下载

微积分 第7版 上 影印版
  • （加）史迪沃特（JAMES STEWART）著 著
  • 出版社： 北京：高等教育出版社
  • ISBN：7040396201
  • 出版时间：2014
  • 标注页数：688页
  • 文件大小：139MB
  • 文件页数：730页
  • 主题词：

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图书目录

A PREVIEW OF CALCULUS1

1 Functions and Models9

1.1 Four Ways to Represent a Function10

1.2 Mathematical Models:A Catalog of Essential Functions23

1.3 New Functions from Old Functions36

1.4 Graphing Calculators and Computers44

1.5 Exponential Functions51

1.6 Inverse Functions and Logarithms58

Review72

Principles of Problem Solving75

2 Limits and Derivatives81

2.1 The Tangent and Velocity Problems82

2.2 The Limit of a Function87

2.3 Calculating Limits Using the Limit Laws99

2.4 The Precise Definition of a Limit108

2.5 Continuity118

2.6 Limits at Infinity;Horizontal Asymptotes130

2.7 Derivatives and Rates of Change143

Writing Project Early Methods for Finding Tangents153

2.8 The Derivative as a Function154

Review165

Problems Plus170

3 Differentiation Rules173

3.1 Derivatives of Polynomials and Exponential Functions174

Applied Project Building a Better Roller Coaster184

3.2 The Product and Quotient Rules184

3.3 Derivatives of Trigonometric Functions191

3.4 The Chain Rule198

Applied Project Where Should a Pilot Start Descent?208

3.5 Implicit Differentiation209

Laboratory Project Families of Implicit Curves217

3.6 Derivatives of Logarithmic Functions218

3.7 Rates of Change in the Natural and Social Sciences224

3.8 Exponential Growth and Decay237

3.9 Related Rates244

3.10 Linear Approximations and Differentials250

Laboratory Project Taylor Polynomials256

3.11 Hyperbolic Functions257

Review264

Problems Plus268

4 Applications of Differentiation273

4.1 Maximum and Minimum Values274

Applied Project The Calculus of Rainbows282

4.2 The Mean Value Theorem284

4.3 How Derivatives Affect the Shape of a Graph290

4.4 Indeterminate Forms and l'Hospital's Rule301

Writing Project The Origins of I'Hospital's Rule310

4.5 Summary of Curve Sketching310

4.6 Graphing with Calculus and Calculators318

4.7 Optimization Problems325

Applied Project The Shape of a Can337

4.8 Newton's Method338

4.9 Antiderivatives344

Review351

Problems Plus355

5 Integrals359

5.1 Areas and Distances360

5.2 The Definite Integral371

Discovery Project Area Functions385

5.3 The Fundamental Theorem of Calculus386

5.4 Indefinite Integrals and the Net Change Theorem397

Writing Project Newton,Leibniz,and the Invention of Calculus406

5.5 The Substitution Rule407

Review415

Problems Plus419

6 Applications of Integration421

6.1 Areas Between Curves422

Applied Project The Gini Index429

6.2 Volumes430

6.3 Volumes by Cylindrical Shells441

6.4 Work446

6.5 Average Value of a Function451

Applied Project Calculus and Baseball455

Applied Project Where to Sit at the Movies456

Review457

Problems Plus459

7 Techniques of Integration463

7.1 Integration by Parts464

7.2 Trigonometric Integrals471

7.3 Trigonometric Substitution478

7.4 Integration of Rational Functions by Partial Fractions484

7.5 Strategy for Integration494

7.6 Integration Using Tables and Computer Algebra Systems500

Discovery Project Patterns in Integrals505

7.7 Approximate Integration506

7.8 Improper Integrals519

Review529

Problems Plus533

8 Further Applications of Integration537

8.1 Arc Length538

Discovery Project Arc Length Contest545

8.2 Area of a Surface of Revolution545

Discovery Project Rotating on a Slant551

8.3 Applications to Physics and Engineering552

Discovery Project Complementary Coffee Cups562

8.4 Applications to Economics and Biology563

8.5 Probability568

Review575

Problems Plus577

9 Differential Equations579

9.1 Modeling with Differential Equations580

9.2 Direction Fields and Euler's Method585

9.3 Separable Equations594

Applied Project How Fast Does a Tank Drain?603

Applied Project Which Is Faster,Going Up or Coming Down?604

9.4 Models for Population Growth605

9.5 Linear Equations616

9.6 Predator-Prey Systems622

Review629

Problems Plus633

10 Parametric Equations and Polar Coordinates635

10.1 Curves Defined by Parametric Equations636

Laboratory Project Running Circles around Circles644

10.2 Calculus with Parametric Curves645

Laboratory Project Bézier Curves653

10.3 Polar Coordinates654

Laboratory Project Families of Polar Curves664

10.4 Areas and Lengths in Polar Coordinates665

10.5 Conic Sections670

10.6 Conic Sections in Polar Coordinates678

Review685

Problems Plus688

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