FINITE (with Mathematics CourseMate with eBook Printed Access Card)
by Berresford, Geoffrey C.; Rockett, Andrew M.
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Summary
Table of Contents
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  
Carbon14 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 GaussJordan Method  
Names for Many Variables  
RowReduced 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 A1  
Introduction to Modeling: Leontief Models  
Linear Programming  
Linear Inequalities  
Inequalities in Two Variables  
Vertices of Feasible Regions  
Bounded and Unbounded Regions  
Applications  
TwoVariable 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  
BoxandWhisker Plot  
Interpreting BoxandWhisker Plots  
Sample Standard Deviation  
Normal Distributions and Binomial Approximation  
Discrete and Continuous Random Variables  
Normal Distribution  
zScores  
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  
TwoPerson 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  
Table of Contents provided by Publisher. All Rights Reserved. 
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