Calculus - Early Transcendentals (International Student Version)

Cover......Page 1
Inside Front Cover......Page 3
Title Page......Page 5
Copyright......Page 6
About the Authors......Page 7
PREFACE......Page 9
SUPPLEMENTS......Page 11
ACKNOWLEDGMENTS......Page 13
Contents......Page 15
THE ROOTS OF CALCULUS......Page 20
FOR THE STUDENT......Page 22
0.1: Functions......Page 23
0.2: New Functions from Old......Page 37
0.3: Families of Functions......Page 49
0.4: Inverse Functions; Inverse Trigonometric Functions......Page 60
0.5: Exponential and Logarithmic Functions......Page 74
1.1: Limits (An Intuitive Approach)......Page 89
1.2: Computing Limits......Page 102
1.3: Limits at Infinity; End Behavior of a Function......Page 111
1.4: Limits (Discussed More Rigorously)......Page 122
1.5: Continuity......Page 132
1.6: Continuity of Trigonometric, Exponential, and Inverse Functions......Page 143
2.1: Tangent Lines and Rates of Change......Page 153
2.2: The Derivative Function......Page 165
2.3: Introduction to Techniques of Differentiation......Page 177
2.4: The Product and Quotient Rules......Page 185
2.5: Derivatives of Trigonometric Functions......Page 191
2.6: The Chain Rule......Page 196
3.1: Implicit Differentiation......Page 207
3.2: Derivatives of Logarithmic Functions......Page 214
3.3: Derivatives of Exponential and Inverse Trigonometric Functions......Page 219
3.4: Related Rates......Page 226
3.5: Local Linear Approximation; Differentials......Page 234
3.6: L'Hôpital's Rule; Indeterminate Forms......Page 241
4.1: Analysis of Functions I: Increase, Decrease, and Concavity......Page 254
4.2: Analysis of Functions II: Relative Extrema; Graphing Polynomials......Page 266
4.3: Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents......Page 276
4.4: Absolute Maxima and Minima......Page 288
4.5: Applied Maximum and Minimum Problems......Page 296
4.6: Rectilinear Motion......Page 310
4.7: Newton's Method......Page 318
4.8: Rolle's Theorem; Mean-Value Theorem......Page 324
5.1: An Overview of the Area Problem......Page 338
5.2: The Indefinite Integral......Page 344
5.3: Integration by Substitution......Page 354
5.4: The Definition of Area as a Limit; Sigma Notation......Page 362
5.5: The Definite Integral......Page 375
5.6: The Fundamental Theorem of Calculus......Page 384
5.7: Rectilinear Motion Revisited Using Integration......Page 398
5.8: Average Value of a Function and its Applications......Page 407
5.9: Evaluating Definite Integrals by Substitution......Page 412
5.10: Logarithmic and Other Functions Defined by Integrals......Page 418
6.1: Area Between Two Curves......Page 435
6.2: Volumes by Slicing; Disks and Washers......Page 443
6.3: Volumes by Cylindrical Shells......Page 454
6.4: Length of a Plane Curve......Page 460
6.5: Area of a Surface of Revolution......Page 466
6.6: Work......Page 471
6.7: Moments, Centers of Gravity, and Centroids......Page 480
6.8: Fluid Pressure and Force......Page 489
6.9: Hyperbolic Functions and Hanging Cables......Page 496
7.1: An Overview of Integration Methods......Page 510
7.2: Integration by Parts......Page 513
7.3: Integrating Trigonometric Functions......Page 522
7.4: Trigonometric Substitutions......Page 530
7.5: Integrating Rational Functions by Partial Fractions......Page 536
7.6: Using Computer Algebra Systems and Tables of Integrals......Page 545
7.7: Numerical Integration; Simpson's Rule......Page 555
7.8: Improper Integrals......Page 569
8.1: Modeling with Differential Equations......Page 583
8.2: Separation of Variables......Page 590
8.3: Slope Fields; Euler's Method......Page 601
8.4: First-Order Differential Equations and Applications......Page 608
9.1: Sequences......Page 618
9.2: Monotone Sequences......Page 629
9.3: Infinite Series......Page 636
9.4: Convergence Tests......Page 645
9.5: The Comparison, Ratio, and Root Tests......Page 653
9.6: Alternating Series; Absolute and Conditional Convergence......Page 660
9.7: Maclaurin and Taylor Polynomials......Page 670
9.8: Maclaurin and Taylor Series; Power Series......Page 681
9.9: Convergence of Taylor Series......Page 690
9.10: Differentiating and Integrating Power Series; Modeling with Taylor Series......Page 700
10.1: Parametric Equations; Tangent Lines and Arc Length for Parametric Curves......Page 714
10.2: Polar Coordinates......Page 727
10.3: Tangent Lines, Arc Length, and Area for Polar Curves......Page 741
10.4: Conic Sections......Page 752
10.5: Rotation of Axes; Second-Degree Equations......Page 770
10.6: Conic Sections in Polar Coordinates......Page 776
11.1: Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces......Page 789
11.2: Vectors......Page 795
11.3: Dot Product; Projections......Page 807
11.4: Cross Product......Page 817
11.5: Parametric Equations of Lines......Page 827
11.6: Planes in 3-Space......Page 835
11.7: Quadric Surfaces......Page 843
11.8: Cylindrical and Spherical Coordinates......Page 854
12.1: Introduction to Vector-Valued Functions......Page 863
12.2: Calculus of Vector-Valued Functions......Page 870
12.3: Change of Parameter; Arc Length......Page 880
12.4: Unit Tangent, Normal, and Binormal Vectors......Page 890
12.5: Curvature......Page 895
12.6: Motion Along a Curve......Page 904
12.7: Kepler's Laws of Planetary Motion......Page 917
13.1: Functions of Two or More Variables......Page 928
13.2: Limits and Continuity......Page 939
13.3: Partial Derivatives......Page 949
13.4: Differentiability, Differentials, and Local Linearity......Page 962
13.5: The Chain Rule......Page 971
13.6: Directional Derivatives and Gradients......Page 982
13.7: Tangent Planes and Normal Vectors......Page 993
13.8: Maxima and Minima of Functions of Two Variables......Page 999
13.9: Lagrange Multipliers......Page 1011
14.1: Double Integrals......Page 1022
14.2: Double Integrals over Nonrectangular Regions......Page 1031
14.3: Double Integrals in Polar Coordinates......Page 1040
14.4: Surface Area; Parametric Surfaces......Page 1048
14.5: Triple Integrals......Page 1061
14.6: Triple Integrals in Cylindrical and Spherical Coordinates......Page 1070
14.7: Change of Variables in Multiple Integrals; Jacobians......Page 1080
14.8: Centers of Gravity Using Multiple Integrals......Page 1093
15.1: Vector Fields......Page 1106
15.2: Line Integrals......Page 1116
15.3: Independence of Path; Conservative Vector Fields......Page 1133
15.4: Green's Theorem......Page 1144
15.5: Surface Integrals......Page 1152
15.6: Applications of Surface Integrals; Flux......Page 1160
15.7: The Divergence Theorem......Page 1170
15.8: Stokes' Theorem......Page 1180
A: Graphing Functions Using Calculators and Computer Algebra Systems......Page 1191
B: Trigonometry Review......Page 1203
C: Solving Polynomial Equations......Page 1217
D: Selected Proofs......Page 1224
Answers to Odd-Numbered Exercises......Page 1235
Index......Page 1289
Inside Back Cover......Page 1315