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Introduction to Analytic Geometry | |

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The Cartesian Coordinate System | |

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The Slope | |

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The Straight Line | |

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Curve Sketching | |

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Discussion of Curves with Graphing Utilities | |

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The Conics | |

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The Circle | |

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The Parabola | |

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The Ellipse | |

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The Hyperbola | |

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Translation of Axes | |

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Standard Equations of the Conics | |

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Review Exercises | |

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Introduction to Calculus: The Derivative | |

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Functions and Intervals | |

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Limits | |

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The Derivative | |

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The Derivative by the Four-Step Process | |

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Derivatives of Polynomials | |

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Instantaneous Rates of Change | |

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Differentiation Formulas | |

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Implicit Differentiation | |

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Higher Derivatives | |

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Review Exercises | |

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Applications of the Derivative | |

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The First-Derivative Test | |

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The Second-Derivative Test | |

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Exploring with Graphing Utilities | |

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Applications of Minima and Maxima | |

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Related rates | |

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Differentials | |

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Review Exercises | |

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The Integral | |

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Antiderivatives | |

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The Area Problem | |

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The Fundamental Theorem of Calculus | |

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The Integral: Notation and General Definition | |

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Basic Integration Formulas | |

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Area Between Curves | |

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Improper Integrals | |

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The Constant of Integration | |

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Numerical Integration | |

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Review Exercises | |

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Application of the Integral | |

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Means of Root Mean Squares | |

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Volumes of Revolution: Disk and Washer Methods | |

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Volumes of Revolution: Shell Method | |

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Centroids | |

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Moments of Inertia | |

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Work and Fluid Pressure | |

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Review Exercises | |

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Derivatives of Transcendental Functions | |

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Review of Trigonometry | |

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Derivatives of Sine and Cosine Functions | |

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Other Trigonometric Functions | |

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Inverse Trigonometric Functions | |

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Derivatives of Inverse Trigonometric Functions | |

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Exponential and Logarithmic Functions | |

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Derivative of the Logarithmic Function | |

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Derivative of the Exponential Function | |

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L'Hospital's rule | |

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Applications | |

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Newton's Method | |

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Review Exercises | |

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Integration Techniques | |

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The Power Formula Again | |

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The Logarithmic and Exponentials Forms | |

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Trigonometric Forms | |

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Further Trigonometric Forms | |

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Inverse Trigonometric Forms | |

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Integration by Trigonometric Substitution | |

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Integration by Parts | |

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Integration of Rational Functions | |

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Integration by Use of Tables | |

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Additional Remarks | |

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Review Exercises | |

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Parametic Equations, Vectors, and Polar Coordinates | |

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Vectors and Parametric Equations | |

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Arc Length | |

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Polar Coordinates | |

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Curves in Polar Coordinates | |

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Areas in Polar Coordinates | |

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Review Exercises | |

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Three-Dimensional Space; Partial Derivatives; Multiple Integrals | |

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Surfaces in Three Dimensions | |

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Partial Derivatives | |

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Applications of Partial Derivatives | |

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Curve Fitting | |

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Integrated Integrals | |

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Volumes by Double Integration | |

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Mass, Centroids, and Moments of Inertia | |

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Volumes in Cylindrical Coordinates | |

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Review Exercises | |

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Infinite Series | |

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Introduction to Infinite Series | |

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Tests for Convergence | |

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Maclaurin Series | |

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Operations with Series | |

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Computations with Series | |

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Applications | |

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Fourier Series | |

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Review Exercises | |

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First-Order Differetial Equations | |

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What is Differential Equation? Separation of Variables | |

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First-Order Linear Differential Equations | |

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Applications of First-Order Differential Equations | |

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Numerical Solutions | |

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Review Exercises | |

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Higher Order Linear Differential Equations | |

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Higher-Order Homogeneous Differential Equations | |

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Auxiliary Equations with Repeating or Complex Roots | |

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Nonhomogeneous Equations | |

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Applications of Second-Order Equations | |

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Review Exercises | |

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The Laplace Transform | |

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Introduction and Basic Properties | |

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Inverse Laplace Transforms | |

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Partial Fractions | |

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Solutions of Linear Equations by Laplace Transforms | |

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Review Exercises | |

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Tables | |

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Common Units of Measure | |

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A Short Table of Integrals | |

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Answers to Selected Exercises | |

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Index | |