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| (Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.) | |
| Preliminaries Real Numbers and the Real Line Lines, Circles, and Parabolas | |
| Functions and Their Graphs | |
| Identifying Functions; Mathematical Models | |
| Combining Functions; Shifting and Scaling Graphs | |
| Trigonometric Functions | |
| Graphing with Calculators and Computers | ... MORE |
| Limits and Derivatives | |
| Rates of Change and Limits | |
| Calculating Limits Using the Limit Laws | |
| Precise Definition of a Limit | |
| One-Sided Limits and Limits at Infinity | |
| Infinite Limits and Vertical Asymptotes | |
| Continuity | |
| Tangents and Derivatives | |
| Differentiation | |
| The Derivative as a Function | |
| Differentiation Rules | |
| The Derivative as a Rate of Change | |
| Derivatives of Trigonometric Functions | |
| The Chain Rule and Parametric Equations | |
| Implicit Differentiation | |
| Related Rates | |
| Linearization and Differentials | |
| Applications of Derivatives | |
| Extreme Values of Functions | |
| The Mean Value Theorem | |
| Monotonic Functions and the First Derivative Test | |
| Concavity and Curve Sketching | |
| Applied Optimization Problems | |
| Indeterminate Forms and L'Hopital's Rule | |
| Newton's Method | |
| Antiderivatives | |
| Integration | |
| Estimating with Finite Sums | |
| Sigma Notation and Limits of Finite Sums | |
| The Definite Integral | |
| The Fundamental Theorem of Calculus | |
| Indefinite Integrals and the Substitution Rule | |
| Substitution and Area Between Curves | |
| Applications of Definite Integrals | |
| Volumes by Slicing and Rotation About an Axis | |
| Volumes by Cylindrical Shells | |
| Lengths of Plane Curves | |
| Moments and Centers of Mass | |
| Areas of Surfaces of Revolution and The Theorems of Pappus | |
| WorkFluid Pressures and Forces | |
| Transcendental Functions | |
| Inverse Functions and their Derivatives | |
| Natural Logarithms | |
| The Exponential Functionax and loga xExponential Growth and Decay | |
| Relative Rates of Growth | |
| Inverse Trigonometric Functions | |
| Hyperbolic Functions | |
| Techniques of Integration | |
| Basic Integration Formulas | |
| Integration by Parts | |
| Integration of Rational Functions by Partial Fractions | |
| Trigonometric Integrals | |
| Trigonometric Substitutions | |
| Integral Tables and Computer Algebra Systems | |
| Numerical Integration | |
| Improper Integrals | |
| Further Applications of Integration | |
| Slope Fields and Separable Differential Equations | |
| First-Order Linear Differential Equations | |
| Euler's Method | |
| Graphical Solutions of Autonomous Equations | |
| Applications of First-Order Differential Equations | |
| Conic Sections and Polar Coordinates | |
| Conic Sections and Quadratic Equations | |
| Classifying Conic Sections by Eccentricity | |
| Quadratic Equations and Rotations | |
| Conics and Parametric Equations; The Cycloid | |
| Polar Coordinates | |
| Graphing in Polar Coordinates | |
| Area and Lengths in Polar Coordinates | |
| Conic Sections in Polar Coordinates | |
| Infinite Sequences and Series | |
| Sequences Infinite Series | |
| The Integral Test | |
| Comparison Tests | |
| The Ratio and Root Tests | |
| Alternating Series, Absolute and Conditional Convergence | |
| Power Series | |
| Taylor and Maclaurin Series | |
| Convergence of Taylor Series; Error Estimates | |
| Applications of Power Series | |
| Fourier Series | |
| Appendices | |
| Mathematical Induction | |
| Proofs of Limit Theorems | |
| Commonly Occurring Limits | |
| Theory of the Real Numbers | |
| Complex Numbers | |
| The Distributive Law for Vector Cross Products | |
| Determinants and Cramer's Rule | |
| Table of Contents provided by Publisher. All Rights Reserved. |