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What is included with this book?
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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