(NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.) | |

P. Preliminaries | |

Real Numbers and the Real Line | |

Coordinates, Lines, and Increments | |

Functions | |

Shifting Graphs | |

Trigonometric Functions | |

Limits and Continuity | |

Rates of Change and Limits | |

Rules for Finding Limits | |

Target Values and Formal Definitions of Limits | |

Extensions of the Limit Concept | |

Continuity | |

Tangent Lines | |

Derivatives | |

The Derivative of a Function | |

Differentiation Rules | |

Rates of Change | |

Derivatives of Trigonometric Functions | |

The Chain Rule | |

Implicit Differentiation and Rational Exponents | |

Related Rates of Change | |

Applications of Derivatives | |

Extreme Values of Functions | |

The Mean Value Theorem | |

The First Derivative Test for Local Extreme Values | |

Graphing with y e and y deg | |

Limits as x aelig; a, Asymptotes, and Dominant Terms | |

Optimization Linearization and Differentials | |

Newton's Method | |

Integration | |

Indefinite Integrals | |

Differential Equations, Initial Value Problems, and Mathematical Modeling | |

Integration by Substitution-Running the Chain Rule Backward | |

Estimating with Finite Sums | |

Riemann Sums and Definite Integrals | |

Properties, Area, and the Mean Value Theorem | |

Substitution in Definite Integrals | |

Numerical Integration | |

Applications of Integrals | |

Areas Between Curves | |

Finding Volumes by Slicing | |

Volumes of Solids of Revolution-Disks and Washers | |

Cylindrical Shells Lengths of Plan Curves | |

Areas of Surfaces of Revolution | |

Moments and Centers of Mass | |

Work | |

Fluid Pressures and Forces | |

The Basic Pattern and Other Modeling Applications | |

Transcendental Functions | |

Inverse Functions and Their Derivatives | |

Natural Logarithms | |

The Exponential Function | |

ax and logax | |

Growth and Decay | |

L'Hocirc;pital's Rule | |

Relative Rates of Growth | |

Inverse Trigonomic Functions | |

Derivatives of Inverse Trigonometric Functions; Integrals | |

Hyperbolic Functions | |

First Order Differential Equations | |

Euler's Numerical Method; Slope Fields | |

Techniques of Integration | |

Basic Integration Formulas | |

Integration by Parts | |

Partial Fractions | |

Trigonometric Substitutions | |

Integral Tables and CAS | |

Improper Integrals | |

Infinite Series | |

Limits of Sequences of Numbers | |

Theorems for Calculating Limits of Sequences | |

Infinite Series | |

The Integral Test for Series of Nonnegative Terms | |

Comparison Tests for Series of Nonnegative Terms | |

The Ratio and Root Tests for Series of Nonnegative Terms | |

Alternating Series, Absolute and Conditional Convergence | |

Power Series | |

Taylor and Maclaurin Series | |

Convergence of Taylor Series; Error Estimates | |

Applications of Power Series | |

Conic Sections, Parametrized Curves, and Polar Coordinates | |

Conic Sections and Quadratic Equations | |

Classifying Conic Sections by Eccentricity | |

Quadratic Equations and Rotations | |

Parametrizations of Plan Curves | |

Calculus with Parametrized Curves | |

Polar Coordinates | |

Graphing in Polar Coordinates | |

Polar Equations for Conic Sections | |

Integration in Polar Coordinates | |

Vectors and Analytic Geometry in Space | |

Vectors in the Plane | |

Cartesian (Rectangular) Coordinates and Vectors in Space | |

Dot Products | |

Cross Products | |

Lines and Planes in Space | |

Cylinders and Quadric Surfaces | |

Cylindrical and Spherical Coordinates | |

Vector-Valued Functions and Motion in Space | |

Vector-Valued Functions and Space Curves | |

Modeling Projectile Motion | |

Arc Length and the Unit Tangent Vector T | |

Curvature, Torison, and the TNB Frame | |

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