微积分 第2版 下2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

微积分 第2版 下PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER 0 PRELIMINARIES1

0.1 The Real Numbers and the Cartesian Plane2

0.2 Lines and Functions11

0.3 Graphing Calculators and Computer Algebra Systems24

0.4 Solving Equations34

0.5 Trigonometric Functions40

0.6 Exponential and Logarithmic Functions50

0.7 Transformations of Functions63

0.8 Preview of Calculus72

CHAPTER 1 LIMITS AND CONTINUITY81

1.1 The Concept of Limit82

1.2 Computation of Limits91

1.3 Continuity and Its Consequences102

1.4 Limits Involving Infinity114

1.5 Formal Definition of the Limit124

1.6 Limits and Loss-of-Significance Errors137

CHAPTER 2 DIFFERENTIATION:ALGEBRAIC,TRIGONOMETRIC,EXPONENTIAL AND LOGARITHMIC FUNCTIONS149

2.1 Tangent Lines and Velocity150

2.2 The Derivative164

2.3 Computation of Derivatives:The Power Rule176

2.4 The Product and Quotient Rules187

2.5 Derivatives of Trigonometric Functions196

2.6 Derivatives of Exponential and Logarithmic Functions205

2.7 The Chain Rule213

2.8 Implicit Differentitiion and Related Rates220

2.9 The Mean Value Theorem229

CHAPTER 3 APPLICATIONS OF DIFFERENTIATION241

3.1 Linear Approximations and L'H pital's Rule242

3.2 Newton's Method251

3.3 Maximum and Minimum Values258

3.4 Increasing and Decreasing Functions269

3.5 Concavity278

3.6 Overview of Curve Sketching286

3.7 Optimization298

3.8 Rates of Change in Applications310

CHAPTER 4 INTEGRATION321

4.1 Antiderivatives322

4.2 Sums and Sigma Notation334

4.3 Area342

4.4 The Definite Integral350

4.5 The Fundamental Theorem of Calculus364

4.6 Integration by Substitution374

4.7 Numerical Integration384

CHAPTER 5 APPLICATIONS OF THE DEFINITE INTEGRAL401

5.1 Area between Curves402

5.2 Volume411

5.3 Volumes by Cylindrical Shells425

5.4 Arc Length and Surface Area434

5.5 Projectile Motion442

5.6 Work,Moments and Hydrostatic Force453

5.7 Probability465

CHAPTER 6 EXPONENTIALS,LOGARITHMS AND OTHER TRANSCENDENTAL FUNCTIONS479

6.1 The Natural Logarithm Revisited480

6.2 Inverse Functions487

6.3 The Exponential Function Revisited495

6.4 Growth and Decay Problems503

6.5 Separable Differential Equations512

6.6 Euler's Method521

6.7 The Inverse Trigonometric Functions530

6.8 The Calculus of the Inverse Trigonometric Functions536

6.9 The Hyperbolic Functions543

CHAPTER 7 INTEGRATION TECHNIQUES555

7.1 Review of Formulas and Techniques556

7.2 Integration by Parts560

7.3 Trigonometric Techniques of Integration568

7.4 Integration of Rational Functions Using Partial Fractions578

7.5 Integration Tables and Computer Algebra Systems586

7.6 Indeterminate Forms and L'H？pital's Rule596

7.7 Improper Integrals604

CHAPTER 8 INFINITE SERIES621

8.1 Sequences of Real Numbers622

8.2 Infinite Series636

8.3 The Integral Test and Comparison Tests647

8.4 Alternating Series658

8.5 Absolute Convergence and the Ratio Test666

8.6 Power Series674

8.7 Taylor Series682

8.8 Applications of Taylor Series695

8.9 Fourier Series703

CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES721

9.1 Plane Curves and Parametric Equations722

9.2 Calculus and Parametric Equations732

9.3 Arc Length and Surface Area in Parametric Equations739

9.4 Polar Coordinates746

9.5 Calculus and Polar Coordinates760

9.6 Conic Sections769

9.7 Conic Sections in Polar Coordinates779

CHAPTER 10 VECTORS AND THE GEOMETRY OF SPACE787

10.1 Vectors in the Plane788

10.2 Vectors in Space798

10.3 The Dot Product805

10.4 The Cross Product814

10.5 Lines and Planes in Space827

10.6 Surfaces in Space.836

CHAPTER 11 VECTOR-VALUED FUNCTIONS851

11.1 Vector-Valued Functions852

11.2 The Calculus of Vector-Valued Functions861

11.3 Motion in Space872

11.4 Curvature882

11.5 Tangent and Normal Vectors890

CHAPTER 12 FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIATION907

12.1 Functions of Several Variables908

12.2 Limits and Continuity924

12.3 Partial Derivatives936

12.4 Tangent Planes and Linear Approximations948

12.5 The Chain Rule960

12.6 The Gradient and Directional Derivatives967

12.7 Extrema of Functions of Several Variables979

12.8 Constrained Optimization and Lagrange Multipliers994

CHAPTER 13 MULTIPLE INTEGRALS1011

13.1 Double Integrals1012

13.2 Area,Volume and Center of Mass1028

13.3 Double Integrals in Polar Coordinates1039

13.4 Surface Area1046

13.5 Triple Integrals1052

13.6 Cylindrical Coordinates1064

13.7 Spherical Coordinates1071

13.8 Change of Variables in Multiple Integrals1079

CHAPTER 14 VECTOR CALCULUS1095

14.1 Vector Fields1096

14.2 Line Integrals1108

14.3 Independence of Path and Conservative Vector Fields1123

14.4 Green's Theorem1134

14.5 Curl and Divergence1143

14.6 Surface Integrals1153

14.7 The Divergence Theorem1167

14.8 Stokes'Theorem1175

APPENDIX A PROOFS OF SELECT THEOREMS1188

APPENDIX B ANSWERS TO ODD-NUMBERED EXERCISES1199

BIBLIOGRAPHY1251

CREDITS1261

INDEX1262