微积分 英文版 原书第9版PDF电子书下载

0　Preliminaries 1

0.1　Real Numbers,Estimation,and Logic 1

0.2　Inequalities and Absolute Values　 8

0.3　The Rectangular Coordinate System　 16

0.4　Graphs of Equations 24

0.5　Functions and Their Graphs　 29

0.6　Operations on Functions 35

0.7　Trigonometric Functions 41

0.8　Chapter Review 51

Review and Preview Problems　 54

1　Limits 55

1.1　Introduction to Limits 55

1.2　Rigorous Study of Limits　 61

1.3　Limit Theorems 68

1.4　Limits Involving Trigonometric Functions 73

1.5　Limits at Infinity;Infinite Limits 77

1.6　Continuity of Functions 82

1.7　Chapter Review 90

Review and Preview Problems 92

2　The Derivative 93

2.1　Two Problems with One Theme 93

2.2　The Derivative 100

2.3　Rules for Finding Derivatives 107

2.4　Derivatives of Trigonometric Functions 114

2.5　The Chain Rule 118

2.6　Higher-Order Derivatives 125

2.7　Implicit Differentiation 130

2.8　Related Rates 135

2.9　Differentials and Approximations 142

2.10　Chapter Review 147

Review and Preview Problems 150

3　Applications of the Derivative 151

3.1　Maxima and Minima 151

3.2　Monotonicity and Concavity 155

3.3　Local Extrema and Extrema on Open Intervals 162

3.4　Practical Problems 167

3.5　Graphing Functions Using Calculus 178

3.6　The Mean Value Theorem for Derivatives 185

3.7　Solving Equations Numerically 190

3.8　Antiderivatives 197

3.9　Introduction to Differential Equations 203

3.10　Chapter Review 209

Review and Preview Problems 214

4　The Definite Integral 215

4.1　Introduction to Area 215

4.2　The Definite Integral 224

4.3　The First Fundamental Theorem of Calculus 232

4.4　The Second Fundamental Theorem of Calculus and the Method of Substitution 243

4.5　The Mean Value Theorem for Integrals and the Use of Symmetry 253

4.6　Numerical Integration 260

4.7　Chapter Review 270

Review and Preview Problems 274

5　Applications of the Integral 275

5.1　The Area of a Plane Region 275

5.2　Volumes of Solids:Slabs,Disks,Washers 281

5.3 Volumes of Solids of Revolution:Shells 288

5.4 Length of a Plane Curve 294

5.5 Work and Fluid Force 301

5.6 Moments and Center of Mass 308

5.7 Probability and Random Variables 316

5.8 Chapter Review 322

Review and Preview Problems 324

6 Transcendental Functions 325

6.1 The Natural Logarithm Function 325

6.2 Inverse Functions and Their Derivatives 331

6.3 The Natural Exponential Function 337

6.4 General Exponential and Logarithmic Functions 342

6.5 Exponential Growth and Decay 347

6.6 First-Order Linear Differential Equations 355

6.7 Approximations for Differential Equations 359

6.8 The Inverse Trigonometric Functions and Their Derivatives 365

6.9 The Hyperbolic Functions and Their Inverses 374

6.10 Chapter Review 380

Review and Preview Problems 382

7 Techniques of Integration 383

7.1 Basic Integration Rules 383

7.2 Integration by Parts 387

7.3 Some Trigonometric Integrals 393

7.4 Rationalizing Substitutions 399

7.5 Integration of Rational Functions Using Partial Fractions 404

7.6 Strategies for Integration 411

7.7 Chapter Review 419

Review and Preview Problems 422

8 Indeterminate Forms and Improper Integrals　 423

8.1　Indeterminate Forms of Type 0/0　 423

8.2　Other Indeterminate Forms　 428

8.3　Improper Integrals:Infinite Limits of Integration　 433

8.4　Improper Integrals:Infinite Integrands　 442

8.5　Chapter Review　 446

Review and Preview Problems　 448

9　Infinite Series　 449

9.1　Infinite Sequences　 449

9.2　Infinite Series　 455

9.3　Positive Series:The Integral Test　 463

9.4　Positive Series:Other Tests　 468

9.5　Alternating Series,Absolute Convergence,and Conditional Convergence　 474

9.6　Power Series　 479

9.7　Operations on Power Series　 484

9.8　Taylor and Maclaurin Series　 489

9.9　The Taylor Approximation to a Function　 497

9.10　Chapter Review　 504

Review and Preview Problems　 508

10　Conics and Polar Coordinates 509

10.1　The Parabola 509

10.2　Ellipses and Hyperbolas　 513

10.3　Translation and Rotation of Axes　 523

10.4　Parametric Representation of Curves in the Plane 530

10.5　The Polar Coordinate System　 537

10.6　Graphs of Polar Equations 542

10.7　Calculus in Polar Coordinates　 547

10.8　Chapter Review 552

Review and Preview Problems　 554

11　Geometry in Space and Vectors 555

11.1　Cartesian Coordinates in Three-Space 555

11.2　Vectors　 560

11.3　The Dot Product 566

11.4　The Cross Product 574

11.5　Vector-Valued Functions and Curvilinear Motion　 579

11.6　Lines and Tangent Lines in Three-Space　 589

11.7　Curvature and Components of Acceleration　 593

11.8　Surfaces in Three-Space　 603

11.9　Cylindrical and Spherical Coordinates 609

11.10　Chapter Review　 613

Review and Preview Problems 616

12　Derivatives for Functions of Two or More Variables 617

12.1　Functions of Two or More Variables　 617

12.2　Partial Derivatives 624

12.3　Limits and Continuity　 629

12.4　Differentiability　 635

12.5　Directional Derivatives and Gradients　 641

12.6　The Chain Rule 647

12.7　Tangent Planes and Approximations　 652

12.8　Maxima and Minima　 657

12.9　The Method of Lagrange Multipliers　 666

12.10　Chapter Review　 672

Review and Preview Problems　 674

13　Multiple Integrals　 675

13.1　Double Integrals over Rectangles 675

13.2　Iterated Integrals　 680

13.3　Double Integrals over Nonrectangular Regions　 684

13.4　Double Integrals in Polar Coordinates　 691

13.5　Applications of Double Integrals　 696

13.6　Surface Area　 700

13.7　Triple Integrals in Cartesian Coordinates 706

13.8　Triple Integrals in Cylindrical and Spherical Coordinates 713

13.9　Change of Variables in Multiple Integrals　 718

13.10　Chapter Review　 728

Review and Preview Problems　 730

14　Vector Calculus　 731

14.1 Vector Fields 731

14.2　Line Integrals　 735

14.3　Independence of Path　 742

14.4　Green's Theorem in the Plane　 749

14.5　Surface Integrals 755

14.6　Gauss's Divergence Theorem　 764

14.7　Stokes's Theorem　 770

14.8　Chapter Review 773

Appendix　A- 1

A.1　Mathematical Induction A- 1

A.2　Proofs of Several Theorems　A- 3