University Calculus - Early Transcendentals (Global Edition)

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 10
Acknowledgments......Page 13
Credits......Page 15
1.1. Functions and Their Graphs......Page 16
1.2. Combining Functions; Shifting and Scaling Graphs......Page 29
1.3. Trigonometric Functions......Page 36
1.4. Graphing with Software......Page 44
1.5. Exponential Functions......Page 48
1.6. Inverse Functions and Logarithms......Page 53
2.1. Rates of Change and Tangents to Curves......Page 66
2.2. Limit of a Function and Limit Laws......Page 73
2.3. The Precise Definition of a Limit......Page 84
2.4. One-Sided Limits......Page 93
2.5. Continuity......Page 100
2.6. Limits Involving Infinity; Asymptotes of Graphs......Page 111
Practice Exercises......Page 125
Additional and Advanced Exercises......Page 127
3.1. Tangents and the Derivative at a Point......Page 130
3.2. The Derivative as a Function......Page 134
3.3. Differentiation Rules......Page 143
3.4. The Derivative as a Rate of Change......Page 153
3.5. Derivatives of Trigonometric Functions......Page 162
3.6. The Chain Rule......Page 168
3.7. Implicit Differentiation......Page 176
3.8. Derivatives of Inverse Functions and Logarithms......Page 181
3.9. Inverse Trigonometric Functions......Page 191
3.10. Related Rates......Page 197
3.11. Linearization and Differentials......Page 205
Questions to Guide Your Review......Page 216
Practice Exercises......Page 217
Additional and Advanced Exercises......Page 221
4.1. Extreme Values of Functions......Page 224
4.2. The Mean Value Theorem......Page 232
4.3. Monotonic Functions and the First Derivative Test......Page 240
4.4. Concavity and Curve Sketching......Page 245
4.5. Indeterminate Forms and L’Hôpital’s Rule......Page 256
4.6. Applied Optimization......Page 265
4.7. Newton’s Method......Page 276
4.8. Antiderivatives......Page 280
Questions to Guide Your Review......Page 290
Practice Exercises......Page 291
Additional and Advanced Exercises......Page 295
5.1. Area and Estimating with Finite Sums......Page 298
5.2. Sigma Notation and Limits of Finite Sums......Page 308
5.3. The Definite Integral......Page 315
5.4. The Fundamental Theorem of Calculus......Page 327
5.5. Indefinite Integrals and the Substitution Method......Page 338
5.6. Definite Integral Substitutions and the Area Between Curves......Page 346
Practice Exercises......Page 356
Additional and Advanced Exercises......Page 359
6.1. Volumes Using Cross-Sections......Page 362
6.2. Volumes Using Cylindrical Shells......Page 373
6.3. Arc Length......Page 381
6.4. Areas of Surfaces of Revolution......Page 387
6.5. Work......Page 391
6.6. Moments and Centers of Mass......Page 397
Practice Exercises......Page 405
Additional and Advanced Exercises......Page 407
7.1. The Logarithm Defined as an Integral......Page 408
7.2. Exponential Change and Separable Differential Equations......Page 418
7.3. Hyperbolic Functions......Page 427
Practice Exercises......Page 435
Additional and Advanced Exercises......Page 436
8. Techniques of Integration......Page 437
8.1. Integration by Parts......Page 438
8.2. Trigonometric Integrals......Page 444
8.3. Trigonometric Substitutions......Page 450
8.4. Integration of Rational Functions by Partial Fractions......Page 455
8.5. Integral Tables and Computer Algebra Systems......Page 462
8.6. Numerical Integration......Page 467
8.7. Improper Integrals......Page 477
Practice Exercises......Page 488
Additional and Advanced Exercises......Page 491
9.1. Sequences......Page 493
9.2. Infinite Series......Page 505
9.3. The Integral Test......Page 514
9.4. Comparison Tests......Page 521
9.5. Absolute Convergence; The Ratio and Root Tests......Page 525
9.6. Alternating Series and Conditional Convergence......Page 531
9.7. Power Series......Page 537
9.8. Taylor and Maclaurin Series......Page 547
9.9. Convergence of Taylor Series......Page 552
9.10. The Binomial Series and Applications of Taylor Series......Page 558
Questions to Guide Your Review......Page 566
Practice Exercises......Page 567
Additional and Advanced Exercises......Page 569
10.1. Parametrizations of Plane Curves......Page 572
10.2. Calculus with Parametric Curves......Page 579
10.3. Polar Coordinates......Page 589
10.4. Graphing Polar Coordinate Equations......Page 593
10.5. Areas and Lengths in Polar Coordinates......Page 596
10.6. Conics in Polar Coordinates......Page 601
Questions to Guide Your Review......Page 607
Practice Exercises......Page 608
Additional and Advanced Exercises......Page 609
11.1. Three-Dimensional Coordinate Systems......Page 611
11.2. Vectors......Page 616
11.3. The Dot Product......Page 625
11.4. The Cross Product......Page 633
11.5. Lines and Planes in Space......Page 639
11.6. Cylinders and Quadric Surfaces......Page 647
Questions to Guide Your Review......Page 652
Practice Exercises......Page 653
Additional and Advanced Exercises......Page 655
12.1. Curves in Space and Their Tangents......Page 657
12.2. Integrals of Vector Functions; Projectile Motion......Page 665
12.3. Arc Length in Space......Page 671
12.4. Curvature and Normal Vectors of a Curve......Page 676
12.5. Tangential and Normal Components of Acceleration......Page 682
12.6. Velocity and Acceleration in Polar Coordinates......Page 684
Practice Exercises......Page 688
Additional and Advanced Exercises......Page 690
13.1. Functions of Several Variables......Page 691
13.2. Limits and Continuity in Higher Dimensions......Page 699
13.3. Partial Derivatives......Page 708
13.4. The Chain Rule......Page 719
13.5. Directional Derivatives and Gradient Vectors......Page 728
13.6. Tangent Planes and Differentials......Page 736
13.7. Extreme Values and Saddle Points......Page 745
13.8. Lagrange Multipliers......Page 754
Questions to Guide Your Review......Page 763
Practice Exercises......Page 764
Additional and Advanced Exercises......Page 767
14.1. Double and Iterated Integrals over Rectangles......Page 770
14.2. Double Integrals over General Regions......Page 775
14.3. Area by Double Integration......Page 784
14.4. Double Integrals in Polar Form......Page 788
14.5. Triple Integrals in Rectangular Coordinates......Page 794
14.6. Moments and Centers of Mass......Page 803
14.7. Triple Integrals in Cylindrical and Spherical Coordinates......Page 810
14.8. Substitutions in Multiple Integrals......Page 821
Practice Exercises......Page 831
Additional and Advanced Exercises......Page 834
15.1. Line Integrals......Page 836
15.2. Vector Fields and Line Integrals: Work, Circulation, and Flux......Page 843
15.3. Path Independence, Conservative Fields, and Potential Functions......Page 855
15.4. Green’s Theorem in the Plane......Page 866
15.5. Surfaces and Area......Page 878
15.6. Surface Integrals......Page 889
15.7. Stokes’ Theorem......Page 900
15.8. The Divergence Theorem and a Unified Theory......Page 912
Practice Exercises......Page 923
Additional and Advanced Exercises......Page 926
A.1. Real Numbers and the Real Line......Page 928
A.2. Mathematical Induction......Page 933
A.3. Lines and Circles......Page 937
A.4. Conic Sections......Page 943
A.5. Proofs of Limit Theorems......Page 951
A.6. Commonly Occurring Limits......Page 954
A.7. Theory of the Real Numbers......Page 955
A.8. Complex Numbers......Page 958
A.9. The Distributive Law for Vector Cross Products......Page 966
A.10. The Mixed Derivative Theorem and the Increment Theorem......Page 968
Answers to Odd-Numbered Exercises......Page 972
Index......Page 1036
A Brief Table of Integrals......Page 1052
Formulas and Theorems......Page 1058
Back Cover......Page 1068