Calculus: Early Transcendental Functions 7th Edition, ISBN-13: 978-1337552516

Description

Calculus: Early Transcendental Functions 7th Edition by Ron Larson, ISBN-13: 978-1337552516

[PDF eBook eTextbook]

1312 pages

Publisher: Cengage Learning; 7 edition (January 1, 2018)

Language: English

ISBN-10: 9781337552516

ISBN-13: 978-1337552516

7th Edition of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS.

Table of contents:

Cover……Page 1

Contents……Page 8

Preface……Page 13

Student Resources……Page 16

Instructor Resources……Page 17

Acknowledgments……Page 18

Chapter 1: Preparation for Calculus……Page 20

1.1 Graphs and Models……Page 21

1.2 Linear Models and Rates of Change……Page 29

1.3 Functions and Their Graphs……Page 38

1.4 Review of Trigonometric Functions……Page 50

1.5 Inverse Functions……Page 60

1.6 Exponential and Logarithmic Functions……Page 71

Review Exercises……Page 79

P.S. Problem Solving……Page 82

Chapter 2: Limits and Their Properties……Page 84

2.1 A Preview of Calculus……Page 85

2.2 Finding Limits Graphically and Numerically……Page 91

2.3 Evaluating Limits Analytically……Page 102

2.4 Continuity and One-Sided Limits……Page 113

2.5 Infinite Limits……Page 126

Review Exercises……Page 134

P.S. Problem Solving……Page 136

Chapter 3: Differentiation……Page 138

3.1 The Derivative and the Tangent Line Problem……Page 139

3.2 Basic Differentiation Rules and Rates of Change……Page 149

3.3 Product and Quotient Rules and Higher-Order Derivatives……Page 162

3.4 The Chain Rule……Page 173

3.5 Implicit Differentiation……Page 188

3.6 Derivatives of Inverse Functions……Page 197

3.7 Related Rates……Page 204

3.8 Newton’s Method……Page 213

Review Exercises……Page 219

P.S. Problem Solving……Page 222

Chapter 4: Applications of Differentiation……Page 224

4.1 Extrema on an Interval……Page 225

4.2 Rolle’s Theorem and the Mean Value Theorem……Page 233

4.3 Increasing and Decreasing Functions and the First Derivative Test……Page 240

4.4 Concavity and the Second Derivative Test……Page 250

4.5 Limits at Infinity……Page 258

4.6 A Summary of Curve Sketching……Page 268

4.7 Optimization Problems……Page 279

4.8 Differentials……Page 290

Review Exercises……Page 297

P.S. Problem Solving……Page 300

Chapter 5: Integration……Page 302

5.1 Antiderivatives and Indefinite Integration……Page 303

5.2 Area……Page 313

5.3 Riemann Sums and Definite Integrals……Page 325

5.4 The Fundamental Theorem of Calculus……Page 336

5.5 Integration by Substitution……Page 351

5.6 Indeterminate Forms and L’Hopital’s Rule……Page 364

5.7 The Natural Logarithmic Function: Integration……Page 375

5.8 Inverse Trigonometric Functions: Integration……Page 384

5.9 Hyperbolic Functions……Page 392

Review Exercises……Page 402

P.S. Problem Solving……Page 404

Chapter 6: Differential Equations……Page 406

6.1 Slope Fields and Euler’s Method……Page 407

6.2 Growth and Decay……Page 416

6.3 Separation of Variables……Page 424

6.4 The Logistic Equation……Page 436

6.5 First-Order Linear Differential Equations……Page 443

6.6 Predator-Prey Differential Equations……Page 450

Review Exercises……Page 457

P.S. Problem Solving……Page 460

Chapter 7: Applications of Integration……Page 462

7.1 Area of a Region between Two Curves……Page 463

7.2 Volume: The Disk Method……Page 473

7.3 Volume: The Shell Method……Page 484

7.4 Arc Length and Surfaces of Revolution……Page 493

7.5 Work……Page 504

7.6 Moments, Centers of Mass, and Centroids……Page 513

7.7 Fluid Pressure and Fluid Force……Page 524

Review Exercises……Page 530

P.S. Problem Solving……Page 532

Chapter 8: Integration Techniques and Improper Integrals……Page 534

8.1 Basic Integration Rules……Page 535

8.2 Integration by Parts……Page 542

8.3 Trigonometric Integrals……Page 551

8.4 Trigonometric Substitution……Page 560

8.5 Partial Fractions……Page 569

8.6 Numerical Integration……Page 578

8.7 Integration by Tables and Other Integration Techniques……Page 585

8.8 Improper Integrals……Page 591

Review Exercises……Page 602

P.S. Problem Solving……Page 604

Chapter 9: Infinite Series……Page 606

9.1 Sequences……Page 607

9.2 Series and Convergence……Page 618

9.3 The Integral Test and p-Series……Page 628

9.4 Comparisons of Series……Page 635

9.5 Alternating Series……Page 642

9.6 The Ratio and Root Tests……Page 650

9.7 Taylor Polynomials and Approximations……Page 659

9.8 Power Series……Page 670

9.9 Representation of Functions by Power Series……Page 680

9.10 Taylor and Maclaurin Series……Page 687

Review Exercises……Page 699

P.S. Problem Solving……Page 702

Chapter 10: Conics, Parametric Equations, and Polar Coordinates……Page 704

10.1 Conics and Calculus……Page 705

10.2 Plane Curves and Parametric Equations……Page 719

10.3 Parametric Equations and Calculus……Page 729

10.4 Polar Coordinates and Polar Graphs……Page 738

10.5 Area and Arc Length in Polar Coordinates……Page 748

10.6 Polar Equations of Conics and Kepler’s Laws……Page 757

Review Exercises……Page 765

P.S. Problem Solving……Page 768

Chapter 11: Vectors and the Geometry of Space……Page 770

11.1 Vectors in the Plane……Page 771

11.2 Space Coordinates and Vectors in Space……Page 781

11.3 The Dot Product of Two Vectors……Page 789

11.4 The Cross Product of Two Vectors in Space……Page 798

11.5 Lines and Planes in Space……Page 806

11.6 Surfaces in Space……Page 817

11.7 Cylindrical and Spherical Coordinates……Page 827

Review Exercises……Page 834

P.S. Problem Solving……Page 836

Chapter 12: Vector-Valued Functions……Page 838

12.1 Vector-Valued Functions……Page 839

12.2 Differentiation and Integration of Vector-Valued Functions……Page 847

12.3 Velocity and Acceleration……Page 855

12.4 Tangent Vectors and Normal Vectors……Page 864

12.5 Arc Length and Curvature……Page 874

Review Exercises……Page 886

P.S. Problem Solving……Page 888

Chapter 13: Functions of Several Variables……Page 890

13.1 Introduction to Functions of Several Variables……Page 891

13.2 Limits and Continuity……Page 903

13.3 Partial Derivatives……Page 913

13.4 Differentials……Page 923

13.5 Chain Rules for Functions of Several Variables……Page 930

13.6 Directional Derivatives and Gradients……Page 938

13.7 Tangent Planes and Normal Lines……Page 950

13.8 Extrema of Functions of Two Variables……Page 959

13.9 Applications of Extrema……Page 967

13.10 Lagrange Multipliers……Page 975

Review Exercises……Page 983

P.S. Problem Solving……Page 986

Chapter 14: Multiple Integration……Page 988

14.1 Iterated Integrals and Area in the Plane……Page 989

14.2 Double Integrals and Volume……Page 997

14.3 Change of Variables: Polar Coordinates……Page 1009

14.4 Center of Mass and Moments of Inertia……Page 1017

14.5 Surface Area……Page 1025

14.6 Triple Integrals and Applications……Page 1032

14.7 Triple Integrals in Other Coordinates……Page 1043

14.8 Change of Variables: Jacobians……Page 1050

Review Exercises……Page 1057

P.S. Problem Solving……Page 1060

Chapter 15: Vector Analysis……Page 1062

15.1 Vector Fields……Page 1063

15.2 Line Integrals……Page 1074

15.3 Conservative Vector Fields and Independence of Path……Page 1088

15.4 Green’s Theorem……Page 1098

15.5 Parametric Surfaces……Page 1107

15.6 Surface Integrals……Page 1117

15.7 Divergence Theorem……Page 1129

15.8 Stokes’s Theorem……Page 1137

Review Exercises……Page 1143

P.S. Problem Solving……Page 1146

Appendix A: Proofs of Selected Theorems……Page 1149

Appedix B: Integration Tables……Page 1150

Appendix C: Precalculus Review……Page 1154

Index……Page 1286

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