Preface x
A Tribute to James Stewart xxii
About the Authors xxiii
Technology in the Ninth Edition xxiv
To the Student xxv
Diagnostic Tests xxvi
A Preview of Calculus
1. Functions and Models
1.1 Inverse Functions and Logarithms 8
2. Limits and Derivatives
2.1 The Limit of a Function 32
2.2 Calculating Limits Using the Limit Laws 44
2.3 The Precise Definition of a Limit 54
2.4 Continuity 64
2.5 Limits at Infinity; Horizontal Asymptotes 76
2.6 Derivatives and Rates of Change 89
2.7 The Derivative as a Function 102
3. Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions 124
3.2 The Product and Quotient Rules 135
3.3 Derivatives of Trigonometric Functions 141
3.4 The Chain Rule 149
3.5 Implicit Differentiation 159
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 167
3.7 Linear Approximations and Differentials 175
3.8 Hyperbolic Functions 183
4. Applications of Differentiation
4.1 Maximum and Minimum Values 202
4.2 The Mean Value Theorem 212
4.3 What Derivatives Tell Us about the Shape of a Graph 218
4.4 Indeterminate Forms and I’Hospital‘s Rule 231
4.5 Optimization Problems 242
4.6 Antiderivatives 257
5. Integrals
5.1 The Area and Distance Problems 274
5.2 The Definite Integral 286
5.3 The Fundamental Theorem of Calculus 301
5.4 Indefinite Integrals and the Net Change Theorem 3 11
5.5 The Substitution Rule 321
6. Applications of Integration
6.1 Areas Between Curves 338
6.2 Volumes 348
6.3 Volumes by Cylindrical Shells 362
6.4 Average Value of a Function 369
7. Techniques of Integration
7.1 Integration by Parts 382
7.2 Trigonometric Integrals 389
7.3 Trigonometric Substitution 396
7.4 Integration of Rational Functions by Partial Fractions 403
7.5 Improper Integrals 413
8. Further Applications of Integration
8.1 Arc Length 430
8.2 Area of a Surface of Revolution 437
8.3 Applications to Physics and Engineering 446
8.4 Applications to Economics and Biology 457
9. Parametric Equations and Polar Coordinates
9.1 Curves Defined by Parametric Equations 468
9.2 Calculus with Parametric Curves 479
9.3 Polar Coordinates 490
9.4 Calculus in Polar Coordinates 500
9.5 Conic Sections 508
10. Sequences, Series, and Power Series
10.1 Sequences 524
10.2 Series 538
10.3 The Integral Test and Estimates of Sums 551
10.4 The Comparison Tests 560
10.5 Alternating Series and Absolute Convergence 565
10.6 The Ratio and Root Tests 576
10.7 Power Series 579
10.8 Representations of Functions as Power Series 584
10.9 Taylor and Maclaurin Series 593
10.10 Applications of Taylor Polynomials 610
11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems 628
11.2 Vectors 634
11.3 The Dot Product 645
11.4 The Cross Product 653
11.5 Equations of Lines and Planes 662
11.6 Cylinders and Quadric Surfaces 673
12. Vector Functions
12.1 Vector Functions and Space Curves 688
12.2 Derivatives and Integrals of Vector Functions 696
12.3 Arc Length and Curvature 702
12.4 Motion in Space: Velocity and Acceleration 714
13. Partial Derivatives
13.1 Functions of Several Variables 732
13.2 Limits and Continuity 749
13.3 Partial Derivatives 759
13.4 Tangent Planes and Linear Approximations 772
13.5 The Chain Rule 783
13.6 Directional Derivatives and the Gradient Vector 792
13.7 Maximum and Minimum Values 806
13.8 Lagrange Multipliers 818
14. Multiple Integrals
14.1 Double Integrals over Rectangles 836
14.2 Double Integrals over General Regions 849
14.3 Double Integrals in Polar Coordinates 860
14.4 Applications of Double Integrals 867
14.5 Surface Area 877
14.6 Triple Integrals 880
14.7 Triple Integrals in Cylindrical Coordinates 893
14.8 Triple Integrals in Spherical Coordinates 900
14.9 Change of Variables in Multiple Integrals 907
15. Vector Calculus
15.1 Vector Fields 922
15.2 Line Integrals 929
15.3 The Fundamental Theorem for Line Integrals 942
15.4 Green’s Theorem 952
15.5 Curl and Divergence 959
15.6 Parametric Surfaces and Their Areas 968
15.7 Surface Integrals 980
15.8 Stokes' Theorem 993
15.9 The Divergence Theorem 999
Appendixes
A Trigonometry A2
B Proofs of Theorems A14
C Answers to Odd-Numbered Exercises A26
