托马斯微积分 上册【正版书籍】 下载 pdf 百度网盘 epub 免费 2025 电子书 mobi 在线

《托马斯微积分》（上）（0版）从Pearson出版公司引进，是一本颇具影响的教材。50多年来，该书平均每4至5年就有一个新版面世，每版较之先前版本都有不少改进之处，体现了这是一部锐意革新的教材；与此同时，该书的一些基本特色始终注意保持且有所增强，说明它又是一部重视继承传统的教材。

Preliminaries

1 Lines 1

2 Functions and Graphs 1 0

3 Exponential Functions 24

4 Inverse Functions and Logarithms 3 1

5 Trigonometric Functions and Their lnverses 44

6 Parametric Equations 60

7 Modeling Change 67

QUESTIONS TO GUIDE YOUR REVIEW 76

PRACTICE EXERCISES 77

ADDITIONAL EXERCISES：THEORY．EXAMPS．APPUCATIONS 80

1 Limits and Continuity

1．1 Rates of Change and Limi85

1．2 Finding Limiand One-Sided Limits 99

1．3 LimiInvolving Infinity 11 2

1．4 Continuity 123

1．5 Tangent Lines 134

QUESTIONS TO GUIDE YOUR REVIEW 1 41

PRACTICE EXERCISES 1 42

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 1 43

2 DeriVatives

2．1 The Derivative as a Functio 147

2．2 The Derivative as a Rate of Change 1 60

2．3 Derivatives of Products．Quotients．and Powers 173

2．4 Derivatives of Trigonometric Functions 1 79

2．5 The ChaiRule and Parametric Equations 1 87

2．6 Implicit Difierentiatio 1 98

2．7 Related Rates 207

QUESTIONS TO GUIDE YOUR REVIEW 21 6

PRACTICE EXERCISES 21 7

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS 221

3 Applications of Derivatives

3．1 Extreme Values of Functions 225

3．2 The McaValue Theorem and Difierential Equations 237

3．3 The Shape of a Graph 245

3．4 Graphical Solutions of Autonomous Differential Equations 257

3．5 Modeling and Optimizatio 266

3．6 Linearizatioand Differentials 283

3．7 Newton’S Method 297

QUESTIONS TO GUIDE YOUR REVIEW 305

PRACTICE EXERCISES 305

ADDITIONAL EXERCISES：THEORY，EXAMPLES．APPLICATIONS 309

4 Integratio

4．1 Indefinite Integrals，Differential Equations．and Modeling 3 1 3

4．2 Integral Rules；Integratioby Substitutio 322

4．3 Estimating with Finite Sums 329

4．4 RicmanSums and Definite Integrals 340

4．5 The McaValue and FundamentaI Theorems 351

4．6 SubStitutioiDefinite Integrals 364

4．7 NumericalIntegratio 373

QUESTIONS TO GUIDE YOUR REVIEW 384

PRACTICE EXERCISES 385

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 389

5 Applications of Integrals

5．1 Volumes by Slicing and RotatioAbout aAs 393

5．2 Modeling Volume Using Cylindrical Shells 406

5．3 Lengths of Plane Curves 41 3

5．4 Springs．Pumping．and Lifting 421

5．5 Fluid Forces 432

5．6 Moments and Centers of Mass 439

QUESTIONS TO GUIDE YOUR REVIEW 451

PRACTICE EXERCISES 45 1

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 454

6 Transcendental Functions and Differential Equations

6．1 Logarithms 457

6．2 Exponential Functions 466

6．3 De|rivatives of Inverse Trigonometric Functions；Integrals 477

6．4 First．Order Separable Differential Equations 485

6．5 Linear FirSt．Order Differential Equations 499

6．6 Euler‘S Method；PoplulatioModels 507

6．7 Hyperbolic Functions 520

QUESTIONS TO GUIDE YOUR REVIEW 530

PRACTICE EXERCISES 531

ADDmONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 535

7 IntegratioTechniques，LH6pital’s Rule，and Improper Integrals

7．1 Basic IntegratioFormulas 539

7．2 Integratioby Parts 546

7．3 Partial Fractions 555

7，4 Trigonometric Substitutions 565

7．5 Integral Tables．Computer Algebra Systems．and

Monte Cario Integratio 570

7．6 LHSpitarS Rule 578

7．7 Improper Integrals 586

QUESTIONS TO GUIDE YOUR REVIEW 600

PRACTICE EXERCISES 601

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 603

8 Infinite Series

8．1 Limis of Sequences of Numbers 608

8．2 Subsequences．Bounded Sequences．and PicardS Method 61 9

8．3 Infinite Series 627

8．4 Series of Nonnegative Terms 1639

8．5 Alternating Series。Absolute and Conditional Convergence 651

8．6 Power Series 660

8．7 Taylor and MaclauriSeries 669

8．8 Applications of Power Series 683

8．9 Fourier Series 691

8．10 Fourier Cosine and Sine Series 698

QUESTIONS TO GUIDE YOUR REVIEW 707

PRACTICE EXERCISES 708

ADDITIONAL EXERCISES：THEORY，EXAMPS．APPLICATIONS 7 11

9 Vectors ithe Plane and Polar Functions

9．1 Vectors ithe Plane 71 7

9．2 Dot Products 728

9．3 Vector-Valued Functions 738

9．4 Modeling Projectile Motio 749

9．5 Polar Coordinates and Graphs 761

9．6 Calculus of Polar Curyes 770

QUESTIONS TO GUIDE YOUR REVIEW 780

PRACTICE EXERCISES 780

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS 784

10 Vectors and M0tioiSpace

1O．1 Cartesian(Rectangular)Coordinates and Vectors iSpace 787

10．2 Dot and Cross Products 796

10．3 Lines and Planes iSpace 807

10．4 cylinders and Ouadric SurfaCes 816

10．5 Vector-Valued Functions and Space Curves 825

10．6 Arc Length and the Unit Tangent Vector T 838

10．7 The TNB Frame；Tangential and Normal Components of Acceleratio

10．8 Plaary Motioand Satellites 857

QUESTIONS TO GUIDE YOUR REVIEW 866

PRACTICE EXERCISES 867

ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 870

11 Multivariable Functions and 111eir Derivatives

1 1．1 Functions of SeveraI Variables 873

11．2 Limits and Continuity iHigher Dimensions 882

11．3 PartiaI Derivatives 890

11．4 The ChaiRule 902

11．5 DirectionaI Derivatives．Gradient Vectors．and Tangent Planes 91 1

11．6 Linearizatioand Difierentials 925

11．7 Extreme Values and Saddle Points 936

……

12 Multiple Integrals

13 IntegratioiVector Fields

Appendices

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