微积分 第5版 下PDF|Epub|txt|kindle电子书版本网盘下载

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A Preview of Calculus2

1 Functions and Models10

1.1Four Ways to Represent a Function11

1.2Mathematical Models：A Catalog of Essential Functions25

1.3New Functions from Old Functions38

1.4Graphing Calculators and Computers48

1.5Exponential Functions55

1.6Inverse Functions and Logarithms63

Review77

Principles of Problem Solving80

2 Limits and Derivatives86

2.1The Tangent and Velocity Problems87

2.2The Limit of a Function92

2.3Calculating Limits Using the Limit Laws104

2.4The Precise Definition of a Limit114

2.5Continuity124

2.6Limits at Infinity；Horizontal Asymptotes135

2.7Tangents，Velocities，and Other Rates of Change149

2.8Derivatives158

Writing Project。Early Methods for Finding Tangents164

2.9The Derivative as a Function165

Review176

Problems Plus180

3 Differentiation Aules182

3.1Derivatives of Polynomials and Exponential Functions183

3.2The Product and Quotient Rules192

3.3Rates of Change in the Natural and Social Sciences199

3.4Derivatives of Trigonometric Functions211

3.5The Chain Rule217

3.6Implicit Differentiation227

3.7Higher Derivatives236

Applied Project。Where Should a Pilot Start Descent?243

Applied Project。Building a Better Roller Goaster243

3.8Derivatives of Logarithmic Functions244

3.9Hyperbolic Functions250

3.10Related Rates256

3.11Linear Approximations and Differentials262

Laboratory Project。Taylor Polynomials269

Review270

Problems Plus274

4 Applications of Differentiation278

4.1Maximum and Minimum Values279

Applied Project。The Calculus of Rainbows288

4.2The Mean Value Theorem290

4.3How Derivatives Affect the Shape of a Graph296

4.4Indeterminate Forms and L’Hospital’s Rule307

Writing Project。The Origins of L’Hospital’s Rule315

4.5Summary of Curve Sketching316

4.6Graphing with Calculus and Calculators324

4.7 Optimization Problems331

Applied Project。The Shape of a Can341

4.8 Applications to Business and Economics342

4.9 Newton’s Method347

4.10Antiderivatives353

Review361

Problems PIus365

5 Integrals368

5.1 Areas and Distances369

5.2 The Definite Integral380

Discovery Project。Area Functions393

5.3 The Fundamental Theorem of Calculus394

5.4 Indefinite Integrals and the Net Change Theorem405

Writing Project。Newton，Leibniz，and the Invention of Galculus413

5.5 The Substitution Rule414

5.6 The Logarithm Defined as an Integral422

Review430

Problems Plus434

6 Applications of lntegration436

6.1 Areas between Curves437

6.2 Volumes444

6.3 Volumes by Cylindrical Shells455

6.4 Work460

6.5 Average Value of a Function464

Applied Project。Where to Sit at the Movies468

Review468

Problems Plus470

7 Techniques of Integration474

7.1Integration by Parts475

7.2Trigonometric Integrals482

7.3Trigonometric Substitution489

7.4Integration of Rational Functions by Partial Fractions496

7.5Strategy for Integration505

7.6Integration Using Tables and Computer Algebra Systems511

Discovery Project 。 Patterns in Integrals517

7.7Approximate Integration518

7.8Improper Integrals530

Review540

Problems Plus543

8 Further Applications of lntegration546

8.1Arc Length547

Discovery Project。Arc Length Contest554

8.2Area of a Surface of Revolution554

Discovery Project 。 Rotating on a 51ant560

8.3Applications to Physics and Engineering561

8.4Applications to Economics and Biology571

8.5Probability575

Review582

Problems Plus584

9 Differential Equations586

9.1Modeling with Differential Equations587

9.2Direction Fields and Euler’s Method592

9.3Separable Equations601

Applied Project。How Fast Does a Tank Drain?609

Applied Project。Which Is Faster，Going Up or Coming Down?610

9.4Exponential Growth and Decay611

Applied Project。Calculus and Baseball622

9.5The Logistic Equation623

9.6Linear Equations632

9.7Predator-Prey Systems638

Review644

Problems Plus648

10 Parametric Equations and Poiar Coordinates650

10.1Curves Defined by Parametric Equations651

Laboratory Project。Running Circles around Circles659

10.2Calculus with Parametric Curves660

Laboratory Project。5ezier Curves669

10.3Polar Coordinates669

10.4Areas and Lengths in Polar Coordinates679

10.5Conic Sections684

10.6Conic Sections in Polar Coordinates692

Review696

Problems Plus699

11 Infinite Sequences and Series700

11.1Sequences701

Laboratory Project。Logistic Sequences713

11.2Series713

11.3The Integral Test and Estimates of Sums723

11.4The Comparison Tests730

11.5Alternating Series735

11.6Absolute Convergence and the Ratio and Root Tests740

11.7Strategy for Testing Series747

11.8Power Series749

11.9Representations of Functions as Power Series754

11.10Taylor and Maclaurin Series760

Laboratory Project。An Elusive Limit772

11.11The Binomial Series772

Writing Project。How Newton Discovered the Binomial 5eriee776

11.12Applications of Taylor Polynomials776

Applied Project。Radiation from the Stars785

Review786

Problems Plue789

12 Vectors and the Geometrq of Space792

12.1Three-Dimensional Coordinate Systems793

12.2Vectors798

12.3The Dot Product807

12.4The Cross Product814

Discovery Project。The Geometry of a Tetrahedron822

12.5Equations of Lines and Planes822

Laboratory Project。Putting 3D in Perspective832

12.6Cylinders and Quadric Surfaces832

12.7Cylindrical and Spherical Coordinates839

Laboratory Project。Families of Surfaces844

Review844

Problems Plus847

13 Vector Functions848

13.1Vector Functions and Space Curves849

13.2Derivatives and Integrals of Vector Functions856

13.3Arc Length and Curvature862

13.4Motion in Space：Velocity and Acceleration870

Applied Project。Kepler’s Laws880

Review881

Problems Plus884

14 Partial DeriVatiVeS886

14.1Functions of Several Variables887

14.2Limits and Continuity902

14.3Partial Derivatives909

14.4Tangent Planes and Linear Approximations923

14.5The Chain Rule931

14.6Directional Derivatives and the Gradient Vector940

14.7Maximum and Minimum Values953

Applied Project。Designing a Dumpster963

Discovery Project。Quadratic Approximations and Critical Points964

14.8Lagrange Multipliers965

Applied ProjectRocket Science972

Applied ProjectHydro-Turbine Optimization973

Review974

Problems Plus978

15 Multiple Integrals980

15.1Double Integrals over Rectangles981

15.2Iterated Integrals989

15.3Double Integrals over General Regions995

15.4Double Integrals in Polar Coordinates1003

15.5Applications of Double Integrals1009

15.6Surface Area1019

15.7Triple Integrals1023

Discovery Project。Volumes of Hyperspheres1032

15.8Triple Integrals in Cylindrical and Spherical Coordinates1033

Applied Project。Roller Derby1039

Discovery Project。The Intersection of Three Cylinders1040

15.9Change of Variables in Multiple Integrals1041

Review1049

Problems Plus1052

16VeCtor CalCUlUS1054

16.1Vector Fields1055

16.2Line Integrals1062

16.3The Fundamental Theorem for Line Integrals1074

16.4Green’s Theorem1083

16.5Curl and Divergence1090

16.6Parametric Surfaces and Their Areas1098

16.7Surface Integrals1109

16.8Stokes’Theorem1121

Writing Project。Three Men and Two Theorems1126

16.9The Divergence Theorem1127

16.10Summary1134

Review1135

Problems Plus1138

17 Second-Drder Differential Equations1140

17.1Second-Order Linear Equations1141

17.2Nonhomogeneous Linear Equations1147

17.3Applications of Second-Order Differential Equations1155

17.4Series Solutions1163

Review1167

AppendixesAl2

ANumbers，Inequalities，and Absolute ValuesA2

BCoordinate Geometry and LinesA10

CGraphs of Second-Degree EquationsA16

DTrigonometryA24

ESigma NotationA34

FProofs of TheoremsA39

GComplex NumbersA49

HAnswers to Odd-Numbered ExercisesA57

IndexA125