Preface 

ix  
Index of Applications 

xv  
Algebra Reference 

Polynomials 

xx  
Factoring 

xxiii  
Rational Expressions 

xxv  
Equations 

xxix  
Inequalities 

xxxv  
Exponents 

xl  
Radicals 

xliv  



Slope and Equations of a Line 


2  (13) 


15  (12) 

Linear Mathematical Models 


27  (10) 

Constructing a Mathematical Model 


37  (19) 


49  (3) 

Extended Application: Using Marginal Cost to Estimate the Cost of Educating Immigrants 


52  (1) 

Extended Application: Depreciation 


53  (3) 

Systems of Linear Equations and Matrices 



Solution of Linear Systems by the Echelon Method 


56  (10) 

Solution of Linear Systems by the GaussJordan Method 


66  (13) 

Addition and Subtraction of Matrices 


79  (8) 

Multiplication of Matrices 


87  (11) 


98  (10) 


108  (14) 


115  (5) 

Extended Application:Contagion 


120  (2) 

Linear Programming:The Graphical Method 



Graphing Linear Inequalities 


122  (8) 

Solving Linear Programming Problems Graphically 


130  (6) 

Applications of Linear Programming 


136  (12) 


144  (4) 

Linear Programming:The Simplex Method 



Slack Variables and the Pivot 


148  (8) 


156  (10) 

Minimization Problems; Duality 


166  (11) 


177  (15) 


186  (1) 

Extended Application: A Minimum Cost Balanced Organic Fertilizer Mix 


187  (5) 



Simple and Compound Interest 


192  (9) 

Future Value of an Annuity 


201  (9) 

Present Value of an Annuity; Amortization 


210  (18) 

A Strategy for Solving Finance Problems 


219  (1) 


220  (4) 

Extended Application: Time, Money, and Polynomials 


224  (4) 




228  (9) 

Applications of Venn Diagrams 


237  (9) 

Introduction to Probability 


246  (8) 

Basic Concepts of Probability 


254  (11) 

Conditional Probability; Independent Events 


265  (16) 


281  (17) 


288  (1) 


289  (6) 

Extended Application: Medical Diagnosis 


295  (3) 

Counting Principles; Further Probability Topics 



The Multiplication Principle; Permutations 


298  (8) 


306  (9) 

Probability Applications of Counting Principles 


315  (10) 


325  (7) 

Probability Distributions; Expected Value 


332  (18) 


343  (5) 

Extended Application: Optimal Inventory for a Service Truck 


348  (2) 



Frequency Distributions; Measures of Central Tendency 


350  (12) 


362  (8) 


370  (10) 

Normal Approximation to the Binomial Distribution 


380  (12) 


387  (5) 



Basic Properties of Markov Chains 


392  (9) 


401  (9) 


410  (16) 


419  (4) 

Extended Application: Cavities and Restoration 


423  (3) 



Strictly Determined Games 


426  (8) 


434  (10) 

Game Theory and Linear Programming 


444  (14) 


451  (3) 

Extended Application: Decision Making in the Military 


454  (4) 




458  (13) 


471  (8) 

Translations and Reflections of Functions 


479  (7) 

Polynomial and Rational Functions 


486  (14) 


500  (11) 


511  (14) 

Applications: Growth and Decay; Mathematics of Finance 


525  (23) 


538  (8) 

Extended Application: Characteristics of the Monkeyface Prickleback 


546  (2) 




548  (17) 


565  (7) 


572  (14) 

Definition of the Derivative 


586  (18) 

Graphical Differentiation 


604  (12) 


610  (6) 

Calculating the Derivative 



Techniques for Finding Derivatives 


616  (13) 

Derivatives of Products and Quotients 


629  (7) 


636  (10) 

Derivatives of Exponential Functions 


646  (6) 

Derivatives of Logarithmic Functions 


652  (10) 


658  (4) 

Graphs and the Derivative 



Increasing and Decreasing Functions 


662  (10) 


672  (13) 

Higher Derivatives, Concavity, and the Second Derivative Test 


685  (14) 


699  (13) 


707  (5) 

Applications of the Derivative 




712  (8) 


720  (11) 

Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand 


731  (9) 


740  (5) 


745  (6) 

Differentials: Linear Approximation 


751  (13) 


757  (3) 

Extended Application: A Total Cost Model for a Training Program 


760  (1) 

Extended Application: The Effect of Oil Price on the Optimal Speed of Ships 


761  (3) 




764  (11) 


775  (8) 

Area and the Definite Integral 


783  (13) 

The Fundamental Theorem of Calculus 


796  (10) 

The Area Between Two Curves 


806  (9) 


815  (17) 


825  (4) 

Extended Application: Estimating Depletion Dates for Minerals 


829  (3) 

Further Techniques and Applications of Integration 



Integration by Parts; Tables of Integrals 


832  (8) 


840  (6) 


846  (8) 


854  (5) 

Solutions of Elementary and Separable Differential Equations 


859  (19) 


871  (3) 

Extended Application: How Much Does a Warranty Cost? 


874  (4) 



Functions of Several Variables 


878  (11) 


889  (10) 


899  (9) 


908  (7) 

Total Differentials and Approximations 


915  (5) 


920  (20) 


932  (5) 

Extended Application: Lagrange Multipliers for a Predator 


937  (3) 



Continuous Probability Models 


940  (7) 

Expected Value and Variance of Continuous Random Variables 


947  (6) 

Special Probability Density Functions 


953  


965  (3) 

Extended Application: A CropPlanting Model 


968  
Tables 


Table 1: Formulas from Geometry 


A1  

Table 2: Area Under a Normal Curve 


A3  


A5  
Answers to Selected Exercises 

A7  
Index 

I1  