Precalculus Review | |

Real Numbers | |

Exponents and Radicals | |

Multiplying and Factoring Algebraic Equations | |

Rational Expressions | |

Solving Polynomial Equations | |

Solving Miscellaneous Equations | |

The Coordinate Plane | |

Functions and Linear Models | |

Functions from the Numerical, Algebraic, and Graphical Viewpoints | |

Applications: Functions and Models | |

Linear Functions and Models | |

Linear Regression | |

Key Concepts | |

Review Exercises | |

Case Study: Modeling Spending on Internet Advertising | |

Technology Guides | |

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |

Nonlinear Functions and Models | |

Quadratic Functions and Models | |

Exponential Functions and Models | |

Logarithmic Functions and Models | |

Logistic Functions and Models | |

Key Concepts | |

Review Exercises | |

Case Study: Checking up on Malthus | |

Technology Guides | |

Optional Internet Topics: Inverse Functions | |

Using and Deriving Algebraic Properties of Logarithms | |

Introduction to the Derivative | |

Limits: Numerical and Graphical Approaches | |

Limits and Continuity | |

Limits: Algebraic Approach | |

Average Rate of Change | |

Derivatives: Numerical and Graphical Viewpoints | |

Derivatives: Algebraic Viewpoint | |

Key Concepts | |

Review Exercises | |

Case Study: Reducing Sulfur Emissions | |

Technology Guides | |

Optional Internet Topics: Sketching the Graph of the Derivative | |

Proof of the Power Rule | |

Continuity and Differentiability | |

Techniques of Differentiation with Applications | |

Derivatives of Powers, Sums, and Constant Multiples | |

A First Application: Marginalnalysis | |

The Product and Quotient Rules | |

The Chain Rule | |

Derivatives of Logarithmic and Exponential Functions | |

Implicit Differentiation | |

Key Concepts | |

Review Exercises | |

Case Study: Projecting Market Growth | |

Technology Guides | |

Optional Internet Topic: Linear Approximation and Error Estimation | |

Further Applications of the Derivative | |

Maxima and Minima | |

Applications of Maxima and Minima | |

Higher Order Derivatives: Acceleration and Concavity | |

Analyzing Graphs | |

Related Rates | |

Elasticity | |

Key Concepts | |

Review Exercises | |

Case Study: Production Lot Size Management | |

Technology Guides | |

The Integral | |

The Indefinite Integral | |

Substitution | |

The Definite Integral: Numerical and Graphical Approaches | |

The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus | |

Key Concepts | |

Review Exercises | |

Case Study: Wage Inflation | |

Technology Guides | |

Optional Internet Topic: Numerical Integration | |

Further Integration Techniques and Applications of the Integral | |

Integration by Parts | |

Area Between Two Curves and Applications | |

Averages and Moving Averages | |

Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams | |

Improper Integrals and Applications | |

Differential Equations and Applications | |

Key Concepts | |

Review Exercises | |

Case Study: Estimating Tax Revenues | |

Technology Guides | |

Optional Internet Topic: Taylor Polynomials | |

Functions of Several Variables | |

Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints | |

Partial Derivatives | |

Maxima and Minima | |

Constrained Maxima and Minima and Applications | |

Double Integrals and Applications | |

Key Concepts | |

Review Exercises | |

Case Study: Modeling Household Income | |

Technology Guides | |

Optional Internet Topic: The Chain Rule for Functions of Several Variables | |

Trigonometric Models | |

Trigonometric Functions, Models, and Regression | |

Derivatives of Trigonometric Functions and Applications | |

Integrals of Trigonometric Functions and Applications | |

Key Concepts | |

Review Exercises | |

Case Study: Predicting Cocoa Inventories | |

Technology Guides | |

Answers to Selected Exercises | |

Index | |

Optional Internet Topic | |

S. Calculus Applied to Probability and Statistics | |

Introduction | |

Continuous Random Variables and Histograms | |

Probability Density Functions: Uniform, Exponential, Normal, and Beta | |

Mean, Median, Variance and Standard Deviation | |

Case Study: Creating a Family Trust | |

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