# Calculus: Early Transcendentals, 10th Edition

# Calculus: Early Transcendentals, 10th Edition

ISBN: 978-0-470-64769-1

Nov 2011

1312 pages

## Description

* Calculus: Early Transcendentals*, 10th Edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds.

*, 10th Edition excels in increasing student comprehension and conceptual understanding of the mathematics. The new edition retains the strengths of earlier editions: e.g., Anton's trademark clarity of exposition; sound mathematics; excellent exercises and examples; and appropriate level, while incorporating more skill and drill problems within*

**Calculus: Early Transcendentals****WileyPLUS**.

The seamless integration of Howard Anton's * Calculus: Early Transcendentals*, 10th Edition with

**WileyPLUS**, a research-based, online environment for effective teaching and learning, continues Anton’s vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.

**WileyPLUS sold separately from text.**

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**0 BEFORE CALCULUS 1**

0.1 Functions 1

0.2 New Functions from Old 15

0.3 Families of Functions 27

0.4 Inverse Functions; Inverse Trigonometric Functions 38

0.5 Exponential and Logarithmic Functions 52

**1 LIMITS AND CONTINUITY 67**

1.1 Limits (An Intuitive Approach) 67

1.2 Computing Limits 80

1.3 Limits at Infinity; End Behavior of a Function 89

1.4 Limits (Discussed More Rigorously) 100

1.5 Continuity 110

1.6 Continuity of Trigonometric, Exponential, and Inverse Functions 121

**2 THE DERIVATIVE 131**

2.1 Tangent Lines and Rates of Change 131

2.2 The Derivative Function 143

2.3 Introduction to Techniques of Differentiation 155

2.4 The Product and Quotient Rules 163

2.5 Derivatives of Trigonometric Functions 169

2.6 The Chain Rule 174

**3 TOPICS IN DIFFERENTIATION 185**

3.1 Implicit Differentiation 185

3.2 Derivatives of Logarithmic Functions 192

3.3 Derivatives of Exponential and Inverse Trigonometric Functions 197

3.4 Related Rates 204

3.5 Local Linear Approximation; Differentials 212

3.6 L’Hôpital’s Rule; Indeterminate Forms 219

**4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 232**

4.1 Analysis of Functions I: Increase, Decrease, and Concavity 232

4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 244

4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 254

4.4 Absolute Maxima and Minima 266

4.5 Applied Maximum and Minimum Problems 274

4.6 Rectilinear Motion 288

4.7 Newton’s Method 296

4.8 Rolle’s Theorem; Mean-Value Theorem 302

**5 INTEGRATION 316**

5.1 An Overview of the Area Problem 316

5.2 The Indefinite Integral 322

5.3 Integration by Substitution 332

5.4 The Definition of Area as a Limit; Sigma Notation 340

5.5 The Definite Integral 353

5.6 The Fundamental Theorem of Calculus 362

5.7 Rectilinear Motion Revisited Using Integration 376

5.8 Average Value of a Function and its Applications 385

5.9 Evaluating Definite Integrals by Substitution 390

5.10 Logarithmic and Other Functions Defined by Integrals 396

**6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 413**

6.1 Area Between Two Curves 413

6.2 Volumes by Slicing; Disks and Washers 421

6.3 Volumes by Cylindrical Shells 432

6.4 Length of a Plane Curve 438

6.5 Area of a Surface of Revolution 444

6.6 Work 449

6.7 Moments, Centers of Gravity, and Centroids 458

6.8 Fluid Pressure and Force 467

6.9 Hyperbolic Functions and Hanging Cables 474

**7 PRINCIPLES OF INTEGRAL EVALUATION 488**

7.1 An Overview of Integration Methods 488

7.2 Integration by Parts 491

7.3 Integrating Trigonometric Functions 500

7.4 Trigonometric Substitutions 508

7.5 Integrating Rational Functions by Partial Fractions 514

7.6 Using Computer Algebra Systems and Tables of Integrals 523

7.7 Numerical Integration; Simpson’s Rule 533

7.8 Improper Integrals 547

**8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 561**

8.1 Modeling with Differential Equations 561

8.2 Separation of Variables 568

8.3 Slope Fields; Euler’s Method 579

8.4 First-Order Differential Equations and Applications 586

**9 INFINITE SERIES 596**

9.1 Sequences 596

9.2 Monotone Sequences 607

9.3 Infinite Series 614

9.4 Convergence Tests 623

9.5 The Comparison, Ratio, and Root Tests 631

9.6 Alternating Series; Absolute and Conditional Convergence 638

9.7 Maclaurin and Taylor Polynomials 648

9.8 Maclaurin and Taylor Series; Power Series 659

9.9 Convergence of Taylor Series 668

9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 678

**10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 692**

10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 692

10.2 Polar Coordinates 705

10.3 Tangent Lines, Arc Length, and Area for Polar Curves 719

10.4 Conic Sections 730

10.5 Rotation of Axes; Second-Degree Equations 748

10.6 Conic Sections in Polar Coordinates 754

**11 THREE-DIMENSIONAL SPACE; VECTORS 767**

11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 767

11.2 Vectors 773

11.3 Dot Product; Projections 785

11.4 Cross Product 795

11.5 Parametric Equations of Lines 805

11.6 Planes in 3-Space 813

11.7 Quadric Surfaces 821

11.8 Cylindrical and Spherical Coordinates 832

**12 VECTOR-VALUED FUNCTIONS 841**

12.1 Introduction to Vector-Valued Functions 841

12.2 Calculus of Vector-Valued Functions 848

12.3 Change of Parameter; Arc Length 858

12.4 Unit Tangent, Normal, and Binormal Vectors 868

12.5 Curvature 873

12.6 Motion Along a Curve 882

12.7 Kepler’s Laws of Planetary Motion 895

**13 PARTIAL DERIVATIVES 906**

13.1 Functions of Two or More Variables 906

13.2 Limits and Continuity 917

13.3 Partial Derivatives 927

13.4 Differentiability, Differentials, and Local Linearity 940

13.5 The Chain Rule 949

13.6 Directional Derivatives and Gradients 960

13.7 Tangent Planes and Normal Vectors 971

13.8 Maxima and Minima of Functions of Two Variables 977

13.9 Lagrange Multipliers 989

**14 MULTIPLE INTEGRALS 1000**

14.1 Double Integrals 1000

14.2 Double Integrals over Nonrectangular Regions 1009

14.3 Double Integrals in Polar Coordinates 1018

14.4 Surface Area; Parametric Surfaces 1026

14.5 Triple Integrals 1039

14.6 Triple Integrals in Cylindrical and Spherical Coordinates 1048

14.7 Change of Variables in Multiple Integrals; Jacobians 1058

14.8 Centers of Gravity Using Multiple Integrals 1071

**15 TOPICS IN VECTOR CALCULUS 1084**

15.1 Vector Fields 1084

15.2 Line Integrals 1094

15.3 Independence of Path; Conservative Vector Fields 1111

15.4 Green’s Theorem 1122

15.5 Surface Integrals 1130

15.6 Applications of Surface Integrals; Flux 1138

15.7 The Divergence Theorem 1148

15.8 Stokes’ Theorem 1158

A APPENDICES

A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS A1

B TRIGONOMETRY REVIEW A13

C SOLVING POLYNOMIAL EQUATIONS A27

D SELECTED PROOFS A34

ANSWERS TO ODD-NUMBERED EXERCISES A45

INDEX I-1

WEB APPENDICES (online only)

Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS.

E REAL NUMBERS, INTERVALS, AND INEQUALITIES

F ABSOLUTE VALUE

G COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS

H DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS

I EARLY PARAMETRIC EQUATIONS OPTION

J MATHEMATICAL MODELS

K THE DISCRIMINANT

L SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS

WEB PROJECTS: Expanding the Calculus Horizon (online only)

Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS.

BLAMMO THE HUMAN CANNONBALL

COMET COLLISION

HURRICANE MODELING

ITERATION AND DYNAMICAL SYSTEMS

RAILROAD DESIGN

ROBOTICS

- Exercise sets have been modified to correspond more closely to questions in Wiley Plus. In addition, more WileyPLUS questions now correspond to specific exercises in the text.
- New applied exercises have been added to the book and existing applied exercises have been updated.
- There will be more rich content – including assignable questions as well as new applets for visualization and exploration – in the WileyPLUS environment.

**Readability Balanced with Rigor:**The authors' goal is to present precise mathematics to the fullest extent possible in an introductory treatment.**Commitment to Student Success:**Clear writing, effective pedagogy--including special exercises designed for self-assessment--and visual representations of the mathematics help students from a variety of backgrounds to learn. Recognizing variations in learning styles, the authors take a ""rule of four"" approach, presenting concepts from the verbal, algebraic, visual, and numerical points of view to foster deeper understanding whenever appropriate.**Dependability:**Anton provides thorough topic coverage organized to fit standard curricula and carefully-constructed exercise sets that users of previous editions have come to depend upon.**Flexibility:**This edition is designed to serve a broad spectrum of calculus philosophies-from traditional to ""reform."" Technology can be emphasized or not, and the order of many topics can be adapted to accommodate each instructor's specific needs.**Quick Check Exercises:**Each exercise set begins with approximately five exercises (answers included) that are designed to provide the student with an immediate assessment of whether he or she has mastered key ideas from the section. They require a minimum of computation and can usually be answered by filling in the blanks.**Focus on Concepts Exercises:**Each exercise set contains a clearly-identified group of problems that focus on the main ideas of the section.**Technology Exercises:**Most sections include exercises that are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or Derive. These exercises are marked with an icon for easy identification.**Expository Excellence:**Clear explanations allow students to build confidence and provide flexibility for the instructor to use class time for problem solving, applications and explanation of difficult concepts.**Mathematical Level:**The book is written at a mathematical level that is suitable for students planning on careers in engineering or science.**Applicability of Calculus:**One of the primary goals of this text is to link calculus to the real world and the student s own experience. This theme is carried through in the examples and exercises.**Historical Notes:**The biographies and historical notes have been a hallmark of this text from its first edition and have been maintained in this edition. All of the biographical materials have been distilled from standard sources with the goal of capturing the personalities of the great mathematicians and bringing them to life for the student.