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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 | |