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 | |

Systems of Linear Equations and Matrices | |

Systems of Two Equations in Two Unknowns | |

Using Matrices to Solve Systems of Equations | |

Applications of Systems of Linear Equations | |

Matrix Algebra and Applications | |

Matrix Addition and Scalar Multiplication | |

Matrix Multiplication | |

Matrix Inversion | |

Game Theory | |

Input-Output Models | |

Linear Programming | |

Graphing Linear Inequalities | |

Solving Linear Programming Problems Graphically | |

The Simplex Method: Solving Standard Maximization Problems | |

The Simplex Method: Solving General Linear Programming Problems | |

The Simplex Method and Duality | |

The Mathematics of Finance | |

Simple Interest | |

Compound Interest | |

Annuities, Loans, and Bonds | |

Sets and Counting | |

Sets and Set Operations | |

Cardinality | |

The Addition and Multiplication Principles | |

Permutations and Combinations | |

Probability | |

Sample Spaces and Events | |

Relative Frequency | |

Probability and Probability Models | |

Probability and Counting Techniques | |

Conditional Probability and Independence | |

Bayes' Theorem and Applications | |

Markov Systems | |

Random Variables and Statistics | |

Random Variables and Distributions | |

Bernoulli Trials and Binomial Random Variables | |

Measures of Central Tendency | |

Measures of Dispersion | |

Normal Distributions | |

Nonlinear Functions and Models | |

Quadratic Functions and Models | |

Exponential Functions and Models | |

Logarithmic Functions and Models | |

Logistic Functions and Models | |

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 | |

Techniques of Differentiation with Applications | |

Derivatives of Powers, Sums, and Constant Multiples | |

A First Application: Marginal Analysis | |

The Product and Quotient Rules | |

The Chain Rule | |

Derivatives of Logarithmic and Exponential Functions | |

Implicit Differentiation | |

Further Applications of the Derivative | |

Maxima and Minima | |

Applications of Maxima and Minima | |

Higher Order Derivatives: Acceleration and Concavity | |

Analyzing Graphs | |

Related Rates | |

Elasticity | |

The Integral | |

The Indefinite Integral | |

Substitution | |

The Definite Integral: Numerical and Graphical Approaches | |

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

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 | |

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 | |

Trigonometric Models | |

Trigonometric Functions, Models, and Regression | |

Derivatives of Trigonometric Functions and Applications | |

Integrals of Trigonometric Functions and Applications | |

Logic | |

Table: Area Under a Normal Curve | |

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 | |

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