P. Preparation For Calculus | |

Graphs and Models | |

Linear Models and Rates of Change | |

Functions and Their Graphs | |

Fitting Models to Data Review Exercises P.S. Problem Solving | |

Limits And Their Properties | |

A Preview of Calculus | |

Finding Limits Graphically and Numerically | |

Evaluating Limits Analytically | |

Continuity and One-Sided Limits | |

Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions Review Exercises P.S. Problem Solving | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

The Product and Quotient Rules and Higher-Order Derivatives | |

The Chain Rule | |

Implicit Differentiation Section Project: Optical Illusions | |

Related Rates Review Exercises P.S. Problem Solving | |

Applications Of Differentiation | |

Extrema on an Interval | |

Rolle's Theorem and the Mean Value Theorem | |

Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |

Concavity and the Second Derivative TeSt. Limits at Infinity | |

A Summary of Curve Sketching | |

Optimization Problems Section Project: Connecticut River | |

Newton's Method | |

Differentials Review Exercises P.S. Problem Solving | |

Integration | |

Antiderivatives and Indefinite Integration | |

Area | |

Riemann Sums and Definite Integrals | |

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |

Integration by Substitution | |

Numerical Integration Review Exercises P.S. Problem Solving | |

Logarithmic, Exponential, And Other Transcendental Functions | |

The Natural Logarithmic Function: Differentiation | |

The Natural Logarithmic Function: Integration | |

Inverse Functions | |

Exponential Functions: Differentiation and Integration | |

Bases Other than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |

Inverse Trigonometric Functions: Differentiation | |

Inverse Trigonometric Functions: Integration | |

Hyperbolic Functions Section Project: St. Louis Arch Review Exercises P.S. Problem Solving | |

Differential Equations | |

Slope Fields and Euler's Method | |

Differential Equations: \Growth and Decay | |

Separation of Variables and the Logistic Equation | |

First-Order Linear Differential Equations Section Project: Weight Loss Review Exercises P.S. Problem Solving | |

Applications of Integration | |

Area of a Region Between Two Curves | |

Volume: The Disk Method | |

Volume: The Shell Method Section Project: Saturn | |

Arc Length and Surfaces of Revolution | |

Work Section Project: Tidal Energy | |

Moments, Centers of Mass, and Centroids | |

Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving | |

Integration Techniques, L'Hopital's Rule, and Improper Integrals | |

Basic Integration Rules | |

Integration by Parts | |

Trigonometric Integrals Section Project: Power Lines | |

Trigonometric Substitution | |

Partial Fractions | |

Integration by Tables and Other Integration Techniques | |

Indeterminate Forms and L'Hopital's Rule | |

Improper Integrals Review Exercises P.S. Problem Solving | |

Infinite Series | |

Sequences | |

Series and Convergence Section Project: Cantor's Disappearing Table | |

The Integral Test and p-Series Section Project: The Harmonic Series | |

Comparisons of Series Section Project: Solera Method | |

Alternating Series | |

The Ratio and Root Tests | |

Taylor Polynomials and Approximations | |

Power Series | |

Representation of Functions by Power Series | |

Taylor and Maclaurin Series Review Exercises P.S. Problem Solving | |

Conics, Parametric Equations, And Polar Coordinates | |

Conics and Calculus | |

Plane Curves and Parametric Equations Section Project: Cycloids | |

Parametric Equations and Calculus | |

Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |

Area and Arc Length in Polar Coordinates | |

Polar Equations of Conics and Kepler's Laws Review Exercises P.S. Problem Solving | |

Book Appendices | |

Proofs of Selected Theorems | |

Integration Tables | |

Online Appendices | |

Precalculus Review (please visit URL to come) | |

Real Numbers and the Real Number Line | |

The Cartesian Plane | |

Review of Trigonometric Functions | |

Rotation and the General Second-Degree Equation (please visit URL to come) | |

Complex Numbers (please visit URL to come) | |

Business and Economic Applications (please visit URL to come) | |

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