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Preliminaries | |

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Lines | |

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Functions and Their Graphs | |

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The Trigonometric Functions | |

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Combining Functions | |

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Graphing Calculators and Computers | |

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Mathematical Models | |

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Chapter Review | |

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Limits | |

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An Intuitive Introduction to Limits | |

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Techniques for Finding Limits | |

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A Precise Definition of a Limit | |

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Continuous Functions | |

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Tangent Lines and Rates of Change | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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The Derivative | |

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The Derivative | |

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Basic Rules of Differentiation | |

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The Product and Quotient Rules | |

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The Role of the Derivative in the Real World | |

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Derivatives of Trigonometric Functions | |

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The Chain Rule | |

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Implicit Differentiation | |

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Related Rates | |

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Differentials and Linear Approximations | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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Applications Of The Derivative | |

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Extrema of Functions | |

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The Mean Value Theorem | |

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Increasing and Decreasing Functions and the FirSt. Derivative TeSt. Concavity and Inflection Points | |

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Limits Involving Infinity | |

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Asymptotes | |

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Curve Sketching | |

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Optimization Problems | |

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Newton's Method | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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Integration | |

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Indefinite Integrals | |

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Integration by Substitution | |

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Area | |

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The Definite Integral | |

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The Fundamental Theorem of Calculus | |

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Numerical Integration | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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Applications Of The Definite Integral | |

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Areas Between Curves | |

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Volumes: Disks, Washers, and Cross Sections | |

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Volumes Using Cylindrical Shells | |

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Arc Length and Areas of Surfaces of Revolution | |

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Work | |

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Fluid Pressure and Force | |

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Moments and Centers of Mass | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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The Transcendental Functions | |

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The Natural Logarithmic Function | |

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Inverse Functions | |

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Exponential Functions | |

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General Exponential and Logarithmic Functions | |

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Inverse Trigonometric Functions | |

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Hyperbolic Functions | |

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Indeterminate Forms and L'H?pital's Rule | |

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Chapter Review | |

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Challenge Problems | |

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Techniques Of Integration | |

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Integration by Parts | |

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Trigonometric Integrals | |

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Trigonometric Substitutions | |

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The Method of Partial Fractions | |

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Integration Using Tables of Integrals and CAS | |

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Improper Integrals | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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Differential Equations | |

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Differential Equations: Separable Equations | |

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Direction Fields and Euler's Method | |

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The Logistic Equation | |

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First-Order Linear Differential Equations | |

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Chapter Review | |

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Challenge Problems | |

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Infinite Sequences And Series | |

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Sequences | |

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Series | |

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The Integral TeSt. The Comparison Tests | |

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Alternating Series | |

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Absolute Convergence | |

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The Ratio and Root Tests | |

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Power Series | |

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Taylor and Maclaurin Series | |

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Approximation by Taylor Polynomials | |

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Chapter Review | |

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Problem-Solving Techniques | |

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Challenge Problems | |

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Conic Sections, Parametric Equations, And Polar Coordinates | |

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Conic Sections | |

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Plane Curves and Parametric Equations | |

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The Calculus of Parametric Equations | |

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Polar Coordinates | |

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Areas and Arc Lengths in Polar Coordinates | |

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Conic Sections in Polar Coordinates | |

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Chapter Review | |

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Challenge Problems | |

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Vectors And The Geometry Of Space | |

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Vectors in the Plane | |

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Coordinate Systems and Vectors in Three-Space | |

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The Dot Product | |

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The Cross Product | |

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Lines and Planes in Space | |

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Surfaces in Space | |

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Cylindrical and Spherical Coordinates | |

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Chapter Review | |

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Challenge Problems | |

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Vector-Valued Functions | |

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Vector-Valued Functions and Space Curves | |

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Differentiation and Integration of Vector- Valued | |

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Functions | |

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Arc Length and Curvature | |

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Velocity and Acceleration | |

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Tangential and Normal Components of Acceleration | |

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Chapter Review | |

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Challenge Problems | |

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Functions Of Several Variables | |

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Functions of Two or More Variables | |

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Limits and Continuity | |

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Partial Derivatives | |

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Differentials | |

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The Chain Rule | |

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Directional Derivatives and Gradient Vectors | |

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Tangent Planes and Normal Lines | |

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Extrema of Functions of Two Variables | |

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Lagrange Multipliers | |

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Chapter Review | |

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Challenge Problems | |

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Multiple Integrals Double Integrals | |

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Iterated Integrals | |

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Double Integrals in Polar Coordinates | |

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Applications of Double Integrals | |

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Surface Area | |

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Triple Integrals | |

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Triple Integrals in Cylindrical and Spherical Coordinates | |

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Change of Variables in Multiple Integrals | |

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Chapter Review | |

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Challenge Problems | |

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Vector Analysis | |

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Vector Fields | |

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Divergence and Curl | |

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Line Integrals | |

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Independence of Path and Conservative Vector Fields | |

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Green's Theorem | |

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Parametric Surfaces | |

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Surface Integrals | |

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The Divergence Theorem | |

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Stoke's Theorem | |

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Chapter Review | |

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Challenge Problems | |

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Appendices | |

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The Real Number Line, Inequalities, and Absolute Value | |

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Proofs of Selected Theorems | |