微积分 英文版 原书第9版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

微积分 英文版 原书第9版PDF格式电子书版下载

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0　Preliminaries1

0.1　Real Numbers,Estimation,and Logic1

0.2　Inequalities and Absolute Values　8

0.3　The Rectangular Coordinate System　16

0.4　Graphs of Equations24

0.5　Functions and Their Graphs　29

0.6　Operations on Functions35

0.7　Trigonometric Functions41

0.8　Chapter Review51

Review and Preview Problems　54

1　Limits55

1.1　Introduction to Limits55

1.2　Rigorous Study of Limits　61

1.3　Limit Theorems68

1.4　Limits Involving Trigonometric Functions73

1.5　Limits at Infinity;Infinite Limits77

1.6　Continuity of Functions82

1.7　Chapter Review90

Review and Preview Problems92

2　The Derivative93

2.1　Two Problems with One Theme93

2.2　The Derivative100

2.3　Rules for Finding Derivatives107

2.4　Derivatives of Trigonometric Functions114

2.5　The Chain Rule118

2.6　Higher-Order Derivatives125

2.7　Implicit Differentiation130

2.8　Related Rates135

2.9　Differentials and Approximations142

2.10　Chapter Review147

Review and Preview Problems150

3　Applications of the Derivative151

3.1　Maxima and Minima151

3.2　Monotonicity and Concavity155

3.3　Local Extrema and Extrema on Open Intervals162

3.4　Practical Problems167

3.5　Graphing Functions Using Calculus178

3.6　The Mean Value Theorem for Derivatives185

3.7　Solving Equations Numerically190

3.8　Antiderivatives197

3.9　Introduction to Differential Equations203

3.10　Chapter Review209

Review and Preview Problems214

4　The Definite Integral215

4.1　Introduction to Area215

4.2　The Definite Integral224

4.3　The First Fundamental Theorem of Calculus232

4.4　The Second Fundamental Theorem of Calculus and the Method of Substitution243

4.5　The Mean Value Theorem for Integrals and the Use of Symmetry253

4.6　Numerical Integration260

4.7　Chapter Review270

Review and Preview Problems274

5　Applications of the Integral275

5.1　The Area of a Plane Region275

5.2　Volumes of Solids:Slabs,Disks,Washers281

5.3 Volumes of Solids of Revolution:Shells288

5.4 Length of a Plane Curve294

5.5 Work and Fluid Force301

5.6 Moments and Center of Mass308

5.7 Probability and Random Variables316

5.8 Chapter Review322

Review and Preview Problems324

6 Transcendental Functions325

6.1 The Natural Logarithm Function325

6.2 Inverse Functions and Their Derivatives331

6.3 The Natural Exponential Function337

6.4 General Exponential and Logarithmic Functions342

6.5 Exponential Growth and Decay347

6.6 First-Order Linear Differential Equations355

6.7 Approximations for Differential Equations359

6.8 The Inverse Trigonometric Functions and Their Derivatives365

6.9 The Hyperbolic Functions and Their Inverses374

6.10 Chapter Review380

Review and Preview Problems382

7 Techniques of Integration383

7.1 Basic Integration Rules383

7.2 Integration by Parts387

7.3 Some Trigonometric Integrals393

7.4 Rationalizing Substitutions399

7.5 Integration of Rational Functions Using Partial Fractions404

7.6 Strategies for Integration411

7.7 Chapter Review419

Review and Preview Problems422

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 Coordinates509

10.1　The Parabola509

10.2　Ellipses and Hyperbolas　513

10.3　Translation and Rotation of Axes　523

10.4　Parametric Representation of Curves in the Plane530

10.5　The Polar Coordinate System　537

10.6　Graphs of Polar Equations542

10.7　Calculus in Polar Coordinates　547

10.8　Chapter Review552

Review and Preview Problems　554

11　Geometry in Space and Vectors555

11.1　Cartesian Coordinates in Three-Space555

11.2　Vectors　560

11.3　The Dot Product566

11.4　The Cross Product574

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 Coordinates609

11.10　Chapter Review　613

Review and Preview Problems616

12　Derivatives for Functions of Two or More Variables617

12.1　Functions of Two or More Variables　617

12.2　Partial Derivatives624

12.3　Limits and Continuity　629

12.4　Differentiability　635

12.5　Directional Derivatives and Gradients　641

12.6　The Chain Rule647

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 Rectangles675

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 Coordinates706

13.8　Triple Integrals in Cylindrical and Spherical Coordinates713

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 Fields731

14.2　Line Integrals　735

14.3　Independence of Path　742

14.4　Green's Theorem in the Plane　749

14.5　Surface Integrals755

14.6　Gauss's Divergence Theorem　764

14.7　Stokes's Theorem　770

14.8　Chapter Review773

Appendix　A-1

A.1　Mathematical Induction A-1

A.2　Proofs of Several Theorems　A-3