Introduction to Analytic Geometry | |

The Cartesian Coordinate System | |

The Slope | |

The Straight Line | |

Curve Sketching | |

Discussion of Curves with Graphing Utilities | |

The Conics | |

The Circle | |

The Parabola | |

The Ellipse | |

The Hyperbola | |

Translation of Axes | |

Standard Equations of the Conics | |

Review Exercises | |

Introduction to Calculus: The Derivative | |

Functions and Intervals | |

Limits | |

The Derivative | |

The Derivative by the Four-Step Process | |

Derivatives of Polynomials | |

Instantaneous Rates of Change | |

Differentiation Formulas | |

Implicit Differentiation | |

Higher Derivatives | |

Review Exercises | |

Applications of the Derivative | |

The First-Derivative Test | |

The Second-Derivative Test | |

Exploring with Graphing Utilities | |

Applications of Minima and Maxima | |

Related rates | |

Differentials | |

Review Exercises | |

The Integral | |

Antiderivatives | |

The Area Problem | |

The Fundamental Theorem of Calculus | |

The Integral: Notation and General Definition | |

Basic Integration Formulas | |

Area Between Curves | |

Improper Integrals | |

The Constant of Integration | |

Numerical Integration | |

Review Exercises | |

Application of the Integral | |

Means of Root Mean Squares | |

Volumes of Revolution: Disk and Washer Methods | |

Volumes of Revolution: Shell Method | |

Centroids | |

Moments of Inertia | |

Work and Fluid Pressure | |

Review Exercises | |

Derivatives of Transcendental Functions | |

Review of Trigonometry | |

Derivatives of Sine and Cosine Functions | |

Other Trigonometric Functions | |

Inverse Trigonometric Functions | |

Derivatives of Inverse Trigonometric Functions | |

Exponential and Logarithmic Functions | |

Derivative of the Logarithmic Function | |

Derivative of the Exponential Function | |

L'Hospital's rule | |

Applications | |

Newton's Method | |

Review Exercises | |

Integration Techniques | |

The Power Formula Again | |

The Logarithmic and Exponentials Forms | |

Trigonometric Forms | |

Further Trigonometric Forms | |

Inverse Trigonometric Forms | |

Integration by Trigonometric Substitution | |

Integration by Parts | |

Integration of Rational Functions | |

Integration by Use of Tables | |

Additional Remarks | |

Review Exercises | |

Parametic Equations, Vectors, and Polar Coordinates | |

Vectors and Parametric Equations | |

Arc Length | |

Polar Coordinates | |

Curves in Polar Coordinates | |

Areas in Polar Coordinates | |

Review Exercises | |

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

Surfaces in Three Dimensions | |

Partial Derivatives | |

Applications of Partial Derivatives | |

Curve Fitting | |

Integrated Integrals | |

Volumes by Double Integration | |

Mass, Centroids, and Moments of Inertia | |

Volumes in Cylindrical Coordinates | |

Review Exercises | |

Infinite Series | |

Introduction to Infinite Series | |

Tests for Convergence | |

Maclaurin Series | |

Operations with Series | |

Computations with Series | |

Applications | |

Fourier Series | |

Review Exercises | |

First-Order Differetial Equations | |

What is Differential Equation? Separation of Variables | |

First-Order Linear Differential Equations | |

Applications of First-Order Differential Equations | |

Numerical Solutions | |

Review Exercises | |

Higher Order Linear Differential Equations | |

Higher-Order Homogeneous Differential Equations | |

Auxiliary Equations with Repeating or Complex Roots | |

Nonhomogeneous Equations | |

Applications of Second-Order Equations | |

Review Exercises | |

The Laplace Transform | |

Introduction and Basic Properties | |

Inverse Laplace Transforms | |

Partial Fractions | |

Solutions of Linear Equations by Laplace Transforms | |

Review Exercises | |

Tables | |

Common Units of Measure | |

A Short Table of Integrals | |

Answers to Selected Exercises | |

Index | |

Table of Contents provided by Publisher. All Rights Reserved. |