University Calculus - Early Transcendentals (Global Edition)

Description

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