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Preface | p. ix |
Functions | p. 1 |
Functions and Their Graphs | p. 1 |
Combining Functions; Shifting and Scaling Graphs | p. 14 |
Trigonometric Functions | p. 22 |
Exponential Functions | p. 30 |
Inverse Functions and Logarithms | p. 36 |
Graphing with Calculators and Computers | p. 50 |
Limits and Continuity | p. 55 |
Rates of Change and Tangents to Curves | p. 55 |
Limit of a Function and Limit Laws | p. 62 |
The Precise Definition of a Limit | p. 74 |
One-Sided Limits and Limits at Infinity | p. 84 |
Infinite Limits and Vertical Asymptotes | p. 97 |
Continuity | p. 103 |
Tangents and Derivatives at a Point | p. 115 |
Questions to Guide Your Review | p. 119 |
Practice Exercises | p. 120 |
Additional and Advanced Exercises | p. 122 |
Differentiation | p. 125 |
The Derivative as a Function | p. 125 |
Differentiation Rules for Polynomials, Exponentials, Products, and Quotients | p. 134 |
The Derivative as a Rate of Change | p. 146 |
Derivatives of Trigonometric Functions | p. 157 |
The Chain Rule and Parametric Equations | p. 164 |
Implicit Differentiation | p. 177 |
Derivatives of Inverse Functions and Logarithms | p. 183 |
Inverse Trigonometric Functions | p. 194 |
Related Rates | p. 201 |
Linearization and Differentials | p. 209 |
Hyperbolic Functions | p. 221 |
Questions to Guide Your Review | p. 227 |
Practice Exercises | p. 228 |
Additional and Advanced Exercises | p. 234 |
Applications of Derivatives | p. 237 |
Extreme Values of Functions | p. 237 |
The Mean Value Theorem | p. 245 |
Monotonic Functions and the First Derivative Test | p. 254 |
Concavity and Curve Sketching | p. 260 |
Applied Optimization | p. 271 |
Indeterminate Forms and L'Hopital's Rule | p. 283 |
Newton's Method | p. 291 |
Antiderivatives | p. 296 |
Questions to Guide Your Review | p. 306 |
Practice Exercises | p. 307 |
Additional and Advanced Exercises | p. 311 |
Integration | p. 315 |
Estimating with Finite Sums | p. 315 |
Sigma Notation and Limits of Finite Sums | p. 325 |
The Definite Integral | p. 332 |
The Fundamental Theorem of Calculus | p. 345 |
Indefinite Integrals and the Substitution Rule | p. 354 |
Substitution and Area Between Curves | p. 360 |
The Logarithm Defined as an Integral | p. 370 |
Questions to Guide Your Review | p. 381 |
Practice Exercises | p. 382 |
Additional and Advanced Exercises | p. 386 |
Applications of Definite Integrals | p. 391 |
Volumes by Slicing and Rotation About an Axis | p. 391 |
Volumes by Cylindrical Shells | p. 401 |
Lengths of Plane Curves | p. 408 |
Areas of Surfaces of Revolution | p. 415 |
Exponential Change and Separable Differential Equations | p. 421 |
Work | p. 430 |
Moments and Centers of Mass | p. 437 |
Questions to Guide Your Review | p. 444 |
Practice Exercises | p. 444 |
Additional and Advanced Exercises | p. 446 |
Techniques of Integration | p. 448 |
Integration by Parts | p. 448 |
Trigonometric Integrals | p. 455 |
Trigonometric Substitutions | p. 461 |
Integration of Rational Functions by Partial Fractions | p. 464 |
Integral Tables and Computer Algebra Systems | p. 471 |
Numerical Integration | p. 477 |
Improper Integrals | p. 487 |
Questions to Guide Your Review | p. 497 |
Practice Exercises | p. 497 |
Additional and Advanced Exercises | p. 500 |
Infinite Sequences and Series | p. 502 |
Sequences | p. 502 |
Infinite Series | p. 515 |
The Integral Test | p. 523 |
Comparison Tests | p. 529 |
The Ratio and Root Tests | p. 533 |
Alternating Series, Absolute and Conditional Convergence | p. 537 |
Power Series | p. 543 |
Taylor and Maclaurin Series | p. 553 |
Convergence of Taylor Series | p. 559 |
The Binomial Series | p. 569 |
Questions to Guide Your Review | p. 572 |
Practice Exercises | p. 573 |
Additional and Advanced Exercises | p. 575 |
Polar Coordinates and Conics | p. 577 |
Polar Coordinates | p. 577 |
Graphing in Polar Coordinates | p. 582 |
Areas and Lengths in Polar Coordinates | p. 586 |
Conic Sections | p. 590 |
Conics in Polar Coordinates | p. 599 |
Conics and Parametric Equations; The Cycloid | p. 606 |
Questions to Guide Your Review | p. 610 |
Practice Exercises | p. 610 |
Additional and Advanced Exercises | p. 612 |
Appendices | p. AP-1 |
Real Numbers and the Real Line | p. AP-1 |
Mathematical Induction | p. AP-7 |
Lines, Circles, and Parabolas | p. AP-10 |
Trigonometry Formulas | p. AP-19 |
Proofs of Limit Theorems | p. AP-21 |
Commonly Occurring Limits | p. AP-25 |
Theory of the Real Numbers | p. AP-26 |
The Distributive Law for Vector Cross Products | p. AP-29 |
The Mixed Derivative Theorem and the Increment Theorem | p. AP-30 |
Answers | p. A-1 |
Index | p. I-1 |
A Brief Table of Integrals | p. T-1 |
Credits | p. C-1 |
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