
Functions and Linear Models 


2  (68) 

Functions from the Numerical and Algebraic Viewpoints 


3  (12) 

Functions from the Graphical Viewpoint 


15  (12) 


27  (11) 


38  (16) 

Linear Regression (optional) 


54  (16) 

You're the Expert Modeling Spending on Internet Advertising 


63  (4) 


67  (3) 



New Functions from Old: Scaled and Shifted Functions 



Systems of Linear Equations and Matrices 


70  (54) 

Systems of Two Linear Equations in Two Unknowns 


71  (14) 

Using Matrices to Solve Systems of Equations 


85  (20) 

Applications of Systems of Linear Equations 


105  (19) 

You're the Expert The Impact of Regulating Sulfur Emissions 


117  (4) 


121  (3) 

Matrix Algebra and Applications 


124  (56) 

Matrix Addition and Scalar Multiplication 


125  (11) 


136  (14) 


150  (11) 


161  (19) 

You're the Expert The Japanese Economy 


175  (2) 


177  (3) 


180  (76) 

Graphing Linear Inequalities 


181  (11) 

Solving Linear Programming Problems Graphically 


192  (17) 

The Simplex Method: Solving Standard Maximization Problems 


209  (18) 

The Simplex Method: Solving General Linear Programming Problems 


227  (13) 

The Simplex Method and Duality (optional) 


240  (16) 

You're the Expert Airline Scheduling 


249  (3) 


252  (4) 

The Mathematics of Finance 


256  (46) 


257  (7) 


264  (12) 

Annuities, Loans, and Bonds 


276  (26) 

You're the Expert Saving for College 


295  (4) 


299  (3) 


302  (46) 


303  (10) 


313  (9) 

The Addition and Multiplication Principles 


322  (9) 

Permutations and Combinations 


331  (17) 

You're the Expert Designing a Puzzle 


343  (2) 


345  (3) 


348  (78) 


349  (13) 


362  (9) 


371  (9) 

Probability and Counting Techniques (optional) 


380  (9) 


389  (8) 

Conditional Probability and Independence 


397  (14) 

Bayes' Theorem and Applications 


411  (15) 

You're the Expert The Monty Hall Problem 


420  (2) 


422  (4) 

Random Variables and Statistics 


426  (60) 

Random Variables and Distributions 


427  (10) 

Bernoulli Trials and Binomial Random Variables 


437  (6) 

Measures of Central Tendency 


443  (12) 


455  (13) 


468  (18) 

You're the Expert Spotting Tax Fraud with Benford's Law 


478  (3) 


481  (5) 



Sampling Distributions and the Central Limit Theorem 






486  (54) 


487  (8) 

Distribution Vectors and Powers of the Transition Matrix 


495  (12) 

LongRange Behavior of Regular Markov Systems 


507  (13) 


520  (20) 

You're the Expert Predicting the Price of Gold 


532  (4) 


536  (4) 


540  (52) 

Quadratic Functions and Models 


541  (8) 

Exponential Functions and Models 


549  (15) 

Logarithmic Functions and Models 


564  (9) 

Trigonometric Functions and Models (optional) 


573  (19) 

You're the Expert Epidemics 


586  (3) 


589  (3) 



Linear and Exponential Regression 



Using and Deriving Algebraic Properties of Logarithms 



Introduction to the Derivative 


592  (76) 


594  (9) 

The Derivative As Rate of Change: A Numerical Approach 


603  (10) 

The Derivative As Slope: A Geometric Approach 


613  (9) 

The Derivative As a Function: An Algebraic Approach 


622  (11) 

A First Application: Marginal Analysis 


633  (9) 

Limits and Continuity: Numerical and Graphical Approaches (optional) 


642  (11) 

Limits and Continuity: Algebraic Approach (optional) 


653  (15) 

You're the Expert Reducing Sulfur Emissions 


661  (3) 


664  (4) 



Sketching the Graph of the Derivative 





Continuity and Differentiability 



Techniques of Differentiation 


668  (58) 

The Product and Quotient Rules 


669  (10) 


679  (11) 

Derivatives of Logarithmic and Exponential Functions 


690  (12) 

Derivatives of Trigonometric Functions (optional) 


702  (7) 


709  (17) 

You're the Expert Projecting Market Growth 


717  (7) 


724  (2) 



Linear Approximation and Error Estimation 



Applications of the Derivative 


726  (58) 


727  (12) 

Applications of Maxima and Minima 


739  (13) 

The Second Derivative and Analyzing Graphs 


752  (12) 


764  (8) 


772  (12) 

You're the Expert Production Lot Size Management 


778  (4) 


782  (2) 


784  (58) 


785  (11) 


796  (9) 

The Definite Integral As a Sum: A Numerical Approach 


805  (10) 

The Definite Integral As Area: A Geometric Approach 


815  (9) 

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


824  (18) 

You're the Expert Wage Inflation 


837  (3) 


840  (2) 





Further Integration Techniques and Applications of the Integral 


842  (58) 


843  (7) 

Area Between Two Curves and Applications 


850  (12) 

Averages and Moving Averages 


862  (10) 

Continuous Income Streams 


872  (5) 

Improper Integrals and Applications 


877  (8) 

Differential Equations and Applications 


885  (15) 

You're the Expert Estimating Tax Revenues 


893  (5) 


898  (2) 

Functions of Several Variables 


900  

Functions of Several Variables from the Numerical and Algebraic Viewpoints 


901  (13) 

ThreeDimensional Space and the Graph of a Function of Two Variables 


914  (11) 


925  (8) 


933  (10) 

Constrained Maxima and Minima and Applications 


943  (11) 


954  

You're the Expert Modeling Household Income 


963  (7) 


970  

Game Theory (Optional Internet Topic) 



TwoPerson Zero Sum Games; Reduction by Dominance 



Strictly Determined Games 





Solving Games using the Simplex Method 



You're the Expert Harvesting Forests 



Introduction to Logic (Optional Internet Topic) 



Statements and Logical Operators 



Logical Equivalence, Tautologies, and Contradictions 



The Conditional and the Biconditional 



Tautological Implications and Tautological Equivalences 







Calculus Applied to Probability and Statistics (Optional Internet Topic) 



Continuous Random Variables and Histograms 



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



Mean, Median, Variance, and Standard Deviation 



You're the Expert Creating a Family Trust 


APPENDIX A Algebra Review 



1  (6) 


7  (7) 

Multiplying and Factoring Algebraic Equations 


14  (5) 


19  (2) 

Solving Polynomial Equations 


21  (6) 

Solving Miscellaneous Equations 


27  (4) 
APPENDIX B Area Under a Normal Curve 

31  (2) 
Answers to Selected Exercises 

33  
Index 

1  