BOOK
University Calculus, Early Transcendentals, Global Edition
Joel R. Hass | Maurice D. Weir | George B. Thomas
(2016)
Additional Information
Book Details
Abstract
For 3-semester or 4-quarter courses in calculus for math, science, and engineering majors.
University Calculus, Early Transcendentals, Third Edition helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.
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Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Title Page | 1 | ||
| Copyright Page | 2 | ||
| Contents | 3 | ||
| Preface | 9 | ||
| Acknowledgments | 12 | ||
| Credits | 14 | ||
| 1. Functions | 15 | ||
| 1.1. Functions and Their Graphs | 15 | ||
| 1.2. Combining Functions; Shifting and Scaling Graphs | 28 | ||
| 1.3. Trigonometric Functions | 35 | ||
| 1.4. Graphing with Software | 43 | ||
| 1.5. Exponential Functions | 47 | ||
| 1.6. Inverse Functions and Logarithms | 52 | ||
| 2. Limits and Continuity | 65 | ||
| 2.1. Rates of Change and Tangents to Curves | 65 | ||
| 2.2. Limit of a Function and Limit Laws | 72 | ||
| 2.3. The Precise Definition of a Limit | 83 | ||
| 2.4. One-Sided Limits | 92 | ||
| 2.5. Continuity | 99 | ||
| 2.6. Limits Involving Infinity; Asymptotes of Graphs | 110 | ||
| Questions to Guide Your Review | 124 | ||
| Practice Exercises | 124 | ||
| Additional and Advanced Exercises | 126 | ||
| 3. Derivatives | 129 | ||
| 3.1. Tangents and the Derivative at a Point | 129 | ||
| 3.2. The Derivative as a Function | 133 | ||
| 3.3. Differentiation Rules | 142 | ||
| 3.4. The Derivative as a Rate of Change | 152 | ||
| 3.5. Derivatives of Trigonometric Functions | 161 | ||
| 3.6. The Chain Rule | 167 | ||
| 3.7. Implicit Differentiation | 175 | ||
| 3.8. Derivatives of Inverse Functions and Logarithms | 180 | ||
| 3.9. Inverse Trigonometric Functions | 190 | ||
| 3.10. Related Rates | 196 | ||
| 3.11. Linearization and Differentials | 204 | ||
| Questions to Guide Your Review | 215 | ||
| Practice Exercises | 216 | ||
| Additional and Advanced Exercises | 220 | ||
| 4. Applications of Derivatives | 223 | ||
| 4.1. Extreme Values of Functions | 223 | ||
| 4.2. The Mean Value Theorem | 231 | ||
| 4.3. Monotonic Functions and the First Derivative Test | 239 | ||
| 4.4. Concavity and Curve Sketching | 244 | ||
| 4.5. Indeterminate Forms and L’Hôpital’s Rule | 255 | ||
| 4.6. Applied Optimization | 264 | ||
| 4.7. Newton’s Method | 275 | ||
| 4.8. Antiderivatives | 279 | ||
| Questions to Guide Your Review | 289 | ||
| Practice Exercises | 290 | ||
| Additional and Advanced Exercises | 294 | ||
| 5. Integrals | 297 | ||
| 5.1. Area and Estimating with Finite Sums | 297 | ||
| 5.2. Sigma Notation and Limits of Finite Sums | 307 | ||
| 5.3. The Definite Integral | 314 | ||
| 5.4. The Fundamental Theorem of Calculus | 326 | ||
| 5.5. Indefinite Integrals and the Substitution Method | 337 | ||
| 5.6. Definite Integral Substitutions and the Area Between Curves | 345 | ||
| Questions to Guide Your Review | 355 | ||
| Practice Exercises | 355 | ||
| Additional and Advanced Exercises | 358 | ||
| 6. Applications of Definite Integrals | 361 | ||
| 6.1. Volumes Using Cross-Sections | 361 | ||
| 6.2. Volumes Using Cylindrical Shells | 372 | ||
| 6.3. Arc Length | 380 | ||
| 6.4. Areas of Surfaces of Revolution | 386 | ||
| 6.5. Work | 390 | ||
| 6.6. Moments and Centers of Mass | 396 | ||
| Questions to Guide Your Review | 404 | ||
| Practice Exercises | 404 | ||
| Additional and Advanced Exercises | 406 | ||
| 7. Integrals and Transcendental Functions | 407 | ||
| 7.1. The Logarithm Defined as an Integral | 407 | ||
| 7.2. Exponential Change and Separable Differential Equations | 417 | ||
| 7.3. Hyperbolic Functions | 426 | ||
| Questions to Guide Your Review | 434 | ||
| Practice Exercises | 434 | ||
| Additional and Advanced Exercises | 435 | ||
| 8. Techniques of Integration | 436 | ||
| 8.1. Integration by Parts | 437 | ||
| 8.2. Trigonometric Integrals | 443 | ||
| 8.3. Trigonometric Substitutions | 449 | ||
| 8.4. Integration of Rational Functions by Partial Fractions | 454 | ||
| 8.5. Integral Tables and Computer Algebra Systems | 461 | ||
| 8.6. Numerical Integration | 466 | ||
| 8.7. Improper Integrals | 476 | ||
| Questions to Guide Your Review | 487 | ||
| Practice Exercises | 487 | ||
| Additional and Advanced Exercises | 490 | ||
| 9. Infinite Sequences and Series | 492 | ||
| 9.1. Sequences | 492 | ||
| 9.2. Infinite Series | 504 | ||
| 9.3. The Integral Test | 513 | ||
| 9.4. Comparison Tests | 520 | ||
| 9.5. Absolute Convergence; The Ratio and Root Tests | 524 | ||
| 9.6. Alternating Series and Conditional Convergence | 530 | ||
| 9.7. Power Series | 536 | ||
| 9.8. Taylor and Maclaurin Series | 546 | ||
| 9.9. Convergence of Taylor Series | 551 | ||
| 9.10. The Binomial Series and Applications of Taylor Series | 557 | ||
| Questions to Guide Your Review | 565 | ||
| Practice Exercises | 566 | ||
| Additional and Advanced Exercises | 568 | ||
| 10. Parametric Equations and Polar Coordinates | 571 | ||
| 10.1. Parametrizations of Plane Curves | 571 | ||
| 10.2. Calculus with Parametric Curves | 578 | ||
| 10.3. Polar Coordinates | 588 | ||
| 10.4. Graphing Polar Coordinate Equations | 592 | ||
| 10.5. Areas and Lengths in Polar Coordinates | 595 | ||
| 10.6. Conics in Polar Coordinates | 600 | ||
| Questions to Guide Your Review | 606 | ||
| Practice Exercises | 607 | ||
| Additional and Advanced Exercises | 608 | ||
| 11. Vectors and the Geometry of Space | 610 | ||
| 11.1. Three-Dimensional Coordinate Systems | 610 | ||
| 11.2. Vectors | 615 | ||
| 11.3. The Dot Product | 624 | ||
| 11.4. The Cross Product | 632 | ||
| 11.5. Lines and Planes in Space | 638 | ||
| 11.6. Cylinders and Quadric Surfaces | 646 | ||
| Questions to Guide Your Review | 651 | ||
| Practice Exercises | 652 | ||
| Additional and Advanced Exercises | 654 | ||
| 12. Vector-Valued Functions and Motion in Space | 656 | ||
| 12.1. Curves in Space and Their Tangents | 656 | ||
| 12.2. Integrals of Vector Functions; Projectile Motion | 664 | ||
| 12.3. Arc Length in Space | 670 | ||
| 12.4. Curvature and Normal Vectors of a Curve | 675 | ||
| 12.5. Tangential and Normal Components of Acceleration | 681 | ||
| 12.6. Velocity and Acceleration in Polar Coordinates | 683 | ||
| Questions to Guide Your Review | 687 | ||
| Practice Exercises | 687 | ||
| Additional and Advanced Exercises | 689 | ||
| 13. Partial Derivatives | 690 | ||
| 13.1. Functions of Several Variables | 690 | ||
| 13.2. Limits and Continuity in Higher Dimensions | 698 | ||
| 13.3. Partial Derivatives | 707 | ||
| 13.4. The Chain Rule | 718 | ||
| 13.5. Directional Derivatives and Gradient Vectors | 727 | ||
| 13.6. Tangent Planes and Differentials | 735 | ||
| 13.7. Extreme Values and Saddle Points | 744 | ||
| 13.8. Lagrange Multipliers | 753 | ||
| Questions to Guide Your Review | 762 | ||
| Practice Exercises | 763 | ||
| Additional and Advanced Exercises | 766 | ||
| 14. Multiple Integrals | 769 | ||
| 14.1. Double and Iterated Integrals over Rectangles | 769 | ||
| 14.2. Double Integrals over General Regions | 774 | ||
| 14.3. Area by Double Integration | 783 | ||
| 14.4. Double Integrals in Polar Form | 787 | ||
| 14.5. Triple Integrals in Rectangular Coordinates | 793 | ||
| 14.6. Moments and Centers of Mass | 802 | ||
| 14.7. Triple Integrals in Cylindrical and Spherical Coordinates | 809 | ||
| 14.8. Substitutions in Multiple Integrals | 820 | ||
| Questions to Guide Your Review | 830 | ||
| Practice Exercises | 830 | ||
| Additional and Advanced Exercises | 833 | ||
| 15. Integrals and Vector Fields | 835 | ||
| 15.1. Line Integrals | 835 | ||
| 15.2. Vector Fields and Line Integrals: Work, Circulation, and Flux | 842 | ||
| 15.3. Path Independence, Conservative Fields, and Potential Functions | 854 | ||
| 15.4. Green’s Theorem in the Plane | 865 | ||
| 15.5. Surfaces and Area | 877 | ||
| 15.6. Surface Integrals | 888 | ||
| 15.7. Stokes’ Theorem | 899 | ||
| 15.8. The Divergence Theorem and a Unified Theory | 911 | ||
| Questions to Guide Your Review | 922 | ||
| Practice Exercises | 922 | ||
| Additional and Advanced Exercises | 925 | ||
| Appendices | 927 | ||
| A.1. Real Numbers and the Real Line | 927 | ||
| A.2. Mathematical Induction | 932 | ||
| A.3. Lines and Circles | 936 | ||
| A.4. Conic Sections | 942 | ||
| A.5. Proofs of Limit Theorems | 950 | ||
| A.6. Commonly Occurring Limits | 953 | ||
| A.7. Theory of the Real Numbers | 954 | ||
| A.8. Complex Numbers | 957 | ||
| A.9. The Distributive Law for Vector Cross Products | 965 | ||
| A.10. The Mixed Derivative Theorem and the Increment Theorem | 967 | ||
| Answers to Odd-Numbered Exercises | 971 | ||
| Index | 1035 | ||
| A Brief Table of Integrals | 1051 | ||
| Formulas and Theorems | 1057 | ||
| Back Cover | Back Cover |