Calculus Early Transcendentals – Howard Anton, Irl Bivens, Stephen Davis – 7th Edition

chapter one FUNCTIONS 11.1 Functions 1

1.2 Graphing Functions Using Calculators and Computer Algebra Systems16

1.3 New Functions from Old 27

1.4 Families of Functions40

1.5 Inverse Functions; Inverse Trigonometric Functions 51

1.6 Exponential and Logarithmic Functions 65

1.7 Mathematical Models 76

1.8 Parametric Equations 86

chapter two LIMITS AND CONTINUITY 101

2.1 Limits (An Intuitive Approach) 101

2.2 Computing Limits 113

2.3 Limits at Infinity; End Behavior of a Function 122

2.4 Limits (Discussed More Rigorously) 134

2.5 Continuity 144

2.6 Continuity of Trigonometric and Inverse Functions 155

chapter three THE DERIVATIVE 165

3.1 Tangent Lines, Velocity, and General Rates of Change 165

3.2 The Derivative Function 178

3.3 Techniques of Differentiation 190

3.4 The Product and Quotient Rules 198

3.5 Derivatives of Trigonometric Functions 204

3.6 The Chain Rule 209

3.7 Related Rates 217

3.8 Local Linear Approximation; Differentials 224

chapter four EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS 235

4.1 Implicit Differentiation 235

4.2 Derivatives of Logarithmic Functions 243

4.3 Derivatives of Exponential and Inverse Trigonometric Functions 248

4.4 L'Hôpital's Rule; Indeterminate Forms 256

chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS 267

5.1 Analysis of Functions I:Increase, Decrease, and Concavity 267

5.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 279

5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology 289

5.4 Absolute Maxima and Minima 301

5.5 Applied Maximum and Minimum Problems 309

5.6 Newton's Method 323

5.7 Rolle's Theorem; Mean-Value Theorem 329

5.8 Rectilinear Motion 336

chapter six INTEGRATION 349

6.1 An Overview of the Area Problem 349

6.2 The Indefinite Integral 355

6.3 Integration by Substitution 365

6.4 The Definition of Area as a Limit; Sigma Notation373

6.5 The Definite Integral 386

6.6 The Fundamental Theorem of Calculus 396

6.7 Rectilinear Motion Revisited Using Integration 410

6.8 Evaluating Definite Integrals by Substitution 419

6.9 Logarithmic Functions from the Integral Point of View 425

chapter 7 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 442

7.1 Area Between Two Curves 442

7.2 Volumes by Slicing; Disks and Washers 450

7.3 Volumes by Cylindrical Shells 459

7.4 Length of a Plane Curve 465

7.5 Area of a Surface of Revolution 471

7.6 Average Value of a Function and its Applications 476

7.7 Work 481

7.8 Fluid Pressure and Force 490

7.9 Hyperbolic Functions and Hanging Cables 496

chapter eight PRINCIPLES OF INTEGRAL EVALUATION 510

8.1 An Overview of Integration Methods 510

8.2 Integration by Parts 513

8.3 Trigonometric Integrals 522

8.4 Trigonometric Substitutions 530

8.5 Integrating Rational Functions by Partial Fractions 537

8.6 Using Computer Algebra Systems and Tables of Integrals 545

8.7 Numerical Integration; Simpson's Rule 556

8.8 Improper Integrals 569

chapter 9 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 582

9.1 First-Order Differential Equations and Applications 582

9.2 Slope Fields; Euler's Method 596

9.3 Modeling with First-Order Differential Equations 603

9.4 Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring 612

chapter ten INFINITE SERIES 624

10.1 Sequences 624

10.2 Monotone Sequences 635

10.3 Infinite Series 643

10.4 Convergence Tests652

10.5 The Comparison, Ratio, and Root Tests 659

10.6 Alternating Series; Conditional Convergence 666

10.7 Maclaurin and Taylor Polynomials 675

10.8 Maclaurin and Taylor Series; PowerSeries 685

10.9 Convergence of Taylor Series 694

10.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 704

chapter eleven ANALYTIC GEOMETRY IN CALCULUS 717

11.1 Polar Coordinates 717

11.2 Tangent Lines and Arc Length for Parametric and Polar Curves 731

11.3 Area in Polar Coordinates 740

11.4 Conic Sections in Calculus 746

11.5 Rotation of Axes; Second-Degree Equations 765

11.6 Conic Sections in Polar Coordinates 771

Horizon Module: Comet Collision 783

chapter twelve THREE-DIMENSIONAL SPACE; VECTORS 786

12.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 786

12.2 Vectors 792

12.3 Dot Product; Projections 804

12.4 Cross Product 813

12.5 Parametric Equations of Lines 824

12.6 Planes in 3-Space 831

12.7 Quadric Surfaces 839

12.8 Cylindrical and Spherical Coordinates 850

chapter thirteen VECTOR-VALUED FUNCTIONS 859

13.1 Introduction to Vector-Valued Functions 859

13.2 Calculus of Vector-Valued Functions 865

13.3 Change of Parameter; Arc Length 876

13.4 Unit Tangent, Normal, and Binormal Vectors 886

13.5 Curvature 892

13.6 Motion Along a Curve 901

13.7 Kepler's Laws of Planetary Motion 914

chapter fourteen PARTIAL DERIVATIVES 924

14.1 Functions of Two or More Variables 924

14.2 Limits and Continuity 936

14.3 Partial Derivatives 945

14.4 Differentiability, Differentials, and Local Linearity 959

14.5 The Chain Rule 968

14.6 Directional Derivatives and Gradients 978

14.7 Tangent Planes and Normal Vectors 989

14.8 Maxima and Minima of Functions of Two Variables 996

14.9 Lagrange Multipliers 1008

chapter fifteen MULTIPLE INTEGRALS 1018

15.1 Double Integrals 1018

15.2 Double Integrals over Nonrectangular Regions 1026

15.3 Double Integrals in Polar Coordinates 1035

15.4 Parametric Surfaces; Surface Area 1043

15.5 Triple Integrals 1056

15.6 Centroid, Center of Gravity, Theorem of Pappus 1065

15.7 Triple Integrals in Cylindrical and Spherical Coordinates 1076

15.8 Change of Variables in Multiple Integrals; Jacobians 1087

Chapter sixteen TOPICS IN VECTOR CALCULUS 1102

16.1 Vector Fields 1102

16.2 Line Integrals 1112

16.3 Independence of Path; Conservative Vector Fields 1129

16.4 Green's Theorem 1139

16.5 Surface Integrals 1147

16.6 Applications of Surface Integrals; Flux 1155

16.7 The Divergence Theorem 1164

16.8 Stokes' Theorem 1173