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Preface | |

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Preliminaries | |

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Precalculus Review | |

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PrecalculusReview II | |

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The Cartesian Coordinate System | |

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Straight Lines | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Functions, Limits, And The Derivative | |

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Functions and Their Graphs | |

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The Algebra of Functions | |

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Functions and Mathematical Models | |

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Portfolio | |

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Using Technology: Finding the Points of Intersection of Two Graphs and Modeling | |

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Limits | |

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Using Technology: Finding the Limit of a Function | |

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One-Sided Limits and Continuity | |

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Using Technology: Finding the Points of Discontinuity of a Function | |

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The Derivative | |

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Using Technology: Graphing a Function and Its Tangent Line | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Differentiation | |

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Basic Rules of Differentiation | |

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Using Technology: Finding the Rate of Change of a Function | |

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The Product and Quotient Rules | |

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Using Technology: The Product and Quotient Rules | |

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The Chain Rule | |

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Using Technology: Finding the Derivative of a Composite Function | |

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Marginal Functions in Economics | |

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Higher-Order Derivatives | |

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Using Technology: Finding the Second Derivative of a Function at a Given Point | |

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Implicit Differentiation and Related Rates | |

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Differentials | |

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Using Technology: Finding the Differential of a Function | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Applications Of The Derivative | |

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Applications of the First Derivative | |

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Using Technology: Using the First Derivative to Analyze a Function | |

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Applications of the Second Derivative | |

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Using Technology: Finding the Inflection Points of a Function | |

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Curve Sketching | |

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Using Technology: Analyzing the Properties of a Optimization | |

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UsingTechnology: Finding the Absolute Extrema of a Function | |

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Optimization II | |

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Summary of Principal Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Exponential And Logarithmic Functions | |

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Exponential Functions | |

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Using Technology | |

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Logarithmic Functions | |

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Compound IntereSt. Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment | |

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Differentiation of Exponential Functions | |

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Using Technology | |

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Differentiation of Logarithmic Functions | |

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Exponential Functions as Mathematical Models | |

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Portfolio | |

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Using Technology: Analyzing Mathematical Models | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Integration | |

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Antiderivatives and the Rules of Integration | |

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Integration by Substitution | |

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Area and the Definite Integral | |

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The Fundamental Theorem of Calculus | |

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Portfolio | |

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Using Technology: Evaluating Definite Integrals | |

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Evaluating Definite Integrals | |

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Using Technology: Evaluating Integrals for Piecewise-Defined Functions | |

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Area between Two Curves | |

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Using Technology: Finding the Area between Two Curves | |

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Applications of the Definite Integral to Business and Economics | |

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Using Technology: Business and Economic Applications/Technology Exercises | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Additional Topics In Integration | |

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Integration by Parts | |

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Integration Using Tables of Integrals | |

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Numerical Integration | |

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Improper Integrals | |

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Applications of Calculus to Probability | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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Calculus Of Several Variables | |

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Functions of Several Variables | |

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Partial Derivatives | |

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Portfolio | |

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Using Technology: Finding Partial Derivatives at a Given Point | |

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Maxima and Minima of Functions of Several Variables | |

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The Method of Least Squares | |

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Using Technology: Finding an Equation of Least-Squares Line | |

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Constrained Maxima and Minima and the Method of Lagrange Multipliers | |

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Double Integrals | |

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Summary of Principal Formulas and Terms | |

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Concept Review Questions | |

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Review Exercises | |

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Before Moving On | |

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The Inverse of a Function | |

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The Graphs of Inverse Functions | |

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Functions That Have Inverses | |

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Finding the Inverse of a Function | |

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Indeterminant Forms and l'H?pital's Rule | |

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The Indeterminant Forms 0/0 and 8/8 | |

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Index | |