Functions | |

Real Numbers, Inequalities, and Lines | |

Real Numbers and Inequalities | |

Sets and Intervals | |

The Cartesian Plane | |

Lines and Slopes | |

Equations of Lines | |

General Linear Equation | |

Exponents | |

Positive Integer Exponents | |

Properties of Exponents | |

Zero and Negative Exponents | |

Roots and Fractional Exponents | |

Fractional Exponents | |

Avoiding Pitfalls in Simplifying | |

Learning Curves in Airplane Production | |

Functions | |

Functions | |

Solving Quadratic Equations | |

Derivation of the Vertex Formula | |

Derivation of the Quadratic Formula | |

More About Functions | |

Polynomial Functions | |

Rational Functions | |

Piecewise Linear Functions | |

Composite Functions | |

Shifts of Graphs | |

Exponential Functions | |

Exponential Functions | |

Compound IntereSt. Depreciation by a Fixed Percentage | |

The Number e | |

Continuous Compounding of IntereSt | |

Intuitive Meaning of Continuous Compounding | |

The Function y = ex | |

Exponential Growth | |

Justification of the Formula for Continuous Compounding | |

Logarithmic Functions | |

Common Logarithms | |

Properties of Common Logarithms | |

Graphs of Logarithmic and Exponential Functions | |

Logarithms to Other Bases | |

Natural Logarithms | |

Carbon-14 Dating | |

Mathematics Of Finance | |

Simple IntereSt | |

Simple Interest Formula | |

Total Amount Due on a Loan | |

Discounted Loans and Effective Interest Rates | |

Compound IntereSt | |

Compound Interest Formula | |

Growth Times | |

Rule of | |

Effective Rates | |

Recap | |

Annuities | |

A First Example | |

Geometric Series | |

Accumulated Account Formula | |

Sinking Funds | |

How Long Will It Take? | |

Amortization | |

Present Value of an Annuity | |

Amortization | |

Unpaid Balance | |

Equity | |

Systems Of Equations And Matrices | |

Systems of Two Linear Equations in Two Variables | |

Systems of Equations | |

Graphical Representations of Equations | |

Equivalent Systems of Equations | |

Elimination Method | |

Matrices and Linear Equations in Two Variables | |

Matrices | |

Augmented Matrices from Systems of Equations | |

Row Operations | |

Solving Equations by Row Reduction | |

Systems of Linear Equations and the Gauss-Jordan Method | |

Names for Many Variables | |

Row-Reduced Form | |

Matrix Arithmetic | |

Equality of Matrices | |

Transpose of a Matrix | |

Identity Matrix | |

Scalar Multiplication | |

Matrix Addition and Subtraction | |

Matrix Multiplication as Evaluation | |

Identity Matrices | |

Matrix Multiplication with Systems of Equations | |

Matrix Multiplication and Row Operations | |

Inverse Matrices and Systems of Linear Equations | |

Inverse Matrices | |

How to Find Inverse Matrices | |

Solving AX = B Using A-1 | |

Introduction to Modeling: Leontief Models | |

Linear Programming | |

Linear Inequalities | |

Inequalities in Two Variables | |

Vertices of Feasible Regions | |

Bounded and Unbounded Regions | |

Applications | |

Two-Variable Linear Programming Problems | |

Linear Programming Problems | |

Fundamental Theorem of Linear Programming | |

Extensions to Larger Problems | |

The Simplex Method for Standard Maximum Problems | |

Standard Maximum Problems | |

Matrix Form of a Standard Maximum Problem | |

The Initial Simplex Tableau | |

Basic and Nonbasic Variables | |

The Pivot Element | |

The Pivot Operation | |

The Simplex Method | |

Standard Minimum Problems and Duality | |

Standard Minimum Problems | |

The Dual of a Standard Minimum Problem | |

Matrix Form | |

Mixed Constraints: A Transportation Problem | |

Probability | |

Sets, Counting, and Venn Diagrams | |

Sets and Set Operations | |

Addition Principle for Counting | |

The Multiplication Principle for Counting | |

The Number of Subsets of a Set | |

Permutations and Combinations | |

Factorials | |

Permutations | |

Combinations | |

Probability Spaces | |

Random Experiments and Sample Spaces | |

Events | |

Probabilities of Possible Outcomes | |

Probabilities of Events | |

Probability That an Event Does Not Occur | |

Probability Space | |

Addition Rule for Probability | |

Conditional Probability and Independence | |

Conditional Probability | |

The Product Rule for Probability | |

Independent Events | |

Bayes' Formula | |

Bayes' Formula | |

Random Variables and Distributions | |

Random Variables | |

Expected Value | |

Binomial Distribution | |

Statistics | |

Random Samples and Data Organization | |

Random Samples | |

Bar Chart | |

Histogram | |

Measures of Central Tendency | |

Mode | |

Median | |

Mean | |

Mean, Median, and Mode | |

Measures of Variation | |

Range | |

Box-and-Whisker Plot | |

Interpreting Box-and-Whisker Plots | |

Sample Standard Deviation | |

Normal Distributions and Binomial Approximation | |

Discrete and Continuous Random Variables | |

Normal Distribution | |

z-Scores | |

The Normal and Binomial Distributions | |

Markov Chains | |

States and Transitions | |

States and Transitions | |

Markov Chains | |

Types of Transition Matrices | |

State Distribution Vectors | |

The kth State Distribution Vector | |

Duration in a Given State | |

Regular Markov Chains | |

Regular Markov Chains | |

The Fundamental Theorem of Regular Markov Chains | |

How to Solve D ? T = D | |

Absorbing Markov Chains | |

Absorbing Markov Chains | |

Standard Form | |

Transition Times and Absorption Probabilities | |

Game Theory | |

Two-Person Games and Saddle Points | |

Payoff Matrix | |

Optimal Strategy | |

Finding Saddle Points | |

Mixed Strategies | |

Mixed Strategies and Expected Values | |

Optimal Mixed Strategies for 2 ? 2 Games | |

Other Interpretations of Mixed Strategies | |

Games and Linear Programming | |

Games as Linear Programming Problems | |

Every Game Has a Solution | |

Index | |

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