Preface 

xi  
Part One A Library of Elementary Functions 

1  (128) 

A Beginning Library of Elementary Functions 


3  (76) 


3  (20) 

Elementary Functions: Graphs and Transformations 


23  (13) 

Linear Functions and Straight Lines 


36  (17) 


53  (26) 

Important Terms and Symbols 


68  (1) 


69  (5) 

Group Activity 1: Introduction to Regression Analysis 


74  (1) 

Group Activity 2: Mathematical Modeling in Business 


75  (4) 

Additional Elementary Functions 


79  (50) 

Polynomial and Rational Functions 


79  (17) 


96  (14) 


110  (19) 

Important Terms and Symbols 


122  (1) 


122  (3) 

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions 


125  (1) 

Group Activity 2: Comparing Regression Models 


125  (4) 
Part Two Finite Mathematics 

129  (380) 


131  (46) 


132  (6) 


138  (13) 

Future Value of an Annuity; Sinking Funds 


151  (8) 

Present Value of an Annuity; Amortization 


159  (18) 

Important Terms and Symbols 


171  (1) 


171  (3) 

Group Activity 1: Reducing Interest Payments on a Home Mortgage 


174  (1) 

Group Activity 2: Yield to Maturity and Internal Rate of Return 


175  (2) 

Systems of Linear Equations; Matrices 


177  (88) 

Review: Systems of Linear Equations in Two Variables 


178  (13) 

Systems of Linear Equations and Augmented Matrices 


191  (10) 


201  (14) 

Matrices: Basic Operations 


215  (14) 

Inverse of a Square Matrix 


229  (11) 

Matrix Equations and Systems of Linear Equations 


240  (10) 

Leontief InputOutput Analysis 


250  (15) 

Important Terms and Symbols 


258  (1) 


259  (3) 

Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit 


262  (1) 

Group Activity 2: Direct and Indirect Operating Costs 


263  (2) 

Linear Inequalities and Linear Programming 


265  (100) 

Systems of Linear Inequalities in Two Variables 


265  (15) 

Linear Programming in Two Dimensions: Geometric Approach 


280  (15) 

Geometric Introduction to the Simplex Method 


295  (8) 

The Simplex Method: Maximization with Problem Constraints of the Form ≤ 


303  (19) 

Dual Problem: Minimization with Problem Constraints of the Form ≥ 


322  (35) 

Maximization and Minimization with Mixed Problem Constraints Important Terms and Symbols 


357  (8) 


358  (3) 

Group Activity 1: The TwoPhase Method (An Alternative to the Big M Method) 


361  (2) 

Group Activity 2: Production Scheduling 


363  (2) 


365  (96) 

Basic Counting Principles 


366  (10) 

Permutations and Combinations 


376  (13) 

Sample Spaces, Events, and Probability 


389  (15) 

Union, Intersection, and Complement of Events; Odds 


404  (14) 

Conditional Probability, Intersection, and Independence 


418  (16) 


434  (7) 

Random Variable, Probability Distribution, and Expected Value 


441  (20) 

Important Terms and Symbols 


451  (1) 


451  (5) 

Group Activity 1: Car and Crying Towels 


456  (2) 

Group Activity 2: Simulation: Draft Lottery for Professional Sports 


458  (3) 


461  (48) 

Properties of Markov Chains 


461  (13) 


474  (12) 


486  (23) 

Important Terms and Symbols 


501  (1) 


502  (3) 

Group Activity 1: Social Mobility 


505  (1) 

Group Activity 2: Gambler' Ruin 


506  (3) 
Part Three A Library of Elementary Functions 

509  (428) 


511  (94) 


512  (12) 


524  (18) 


542  (13) 

Derivatives of Constants, Power Forms, and Sums 


555  (14) 

Derivatives of Products and Quotients 


569  (8) 


577  (7) 

Marginal Analysis in Business and Economics 


584  (21) 

Important Terms and Symbols 


596  (1) 

Summary of Rules of Differentiation 


596  (1) 


597  (4) 

Group Activity 1: Minimal Average Cost 


601  (1) 

Group Activity 2: Numerical Differentiation on a Graphing Utility 


602  (3) 

Graphing and Optimization 


605  (90) 


606  (16) 

First Derivative and Graphs 


622  (17) 

Second Derivative and Graphs 


639  (16) 

Curve Sketching Techniques: Unified and Extended 


655  (17) 

Optimization; Absolute Maxima and Minima 


672  (23) 

Important Terms and Symbols 


688  (1) 


689  (4) 

Group Activity 1: Maximizing Profit 


693  (1) 

Group Activity 2: Minimizing Construction Costs 


693  (2) 

Additional Derivative Topics 


695  (48) 

The Constant e and Continuous Compound Interest 


695  (7) 

Derivatives of Logarithmic and Exponential Functions 


702  (12) 


714  (11) 


725  (7) 


732  (11) 

Important Terms and Symbols 


738  (1) 

Additional Rules of Differentiation 


738  (1) 


738  (2) 

Group Activity 1: Elasticity of Demand 


740  (1) 

Group Activity 2: Point of Diminishing Returns 


741  (2) 


743  (82) 

Antiderivatives and Indefinite Integrals 


743  (15) 

Integration by Substitution 


758  (12) 

Differential Equaitons; Growth and Decay 


770  (11) 

GeometricNumeric Introduction to the Definite Integral 


781  (16) 

Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus 


797  (28) 

Important Terms and Symbols 


815  (1) 

Integration Formulas and Properties 


816  (1) 


816  (4) 

Group Activity 1: Simpson's Rule 


820  (3) 

Group Activity 2: BellShaped Curves 


823  (2) 

Additional Integration Topics 


825  (44) 


825  (11) 

Applications in Business and Economics 


836  (13) 


849  (8) 


857  (12) 

Important Terms and Symbols 


864  (1) 


865  (2) 

Group Activity 1: Analysis of Income Concentration from Raw Data 


867  (1) 

Group Activity 2: Grain Exchange 


868  (1) 


869  (68) 

Functions of Several Variables 


869  (11) 


880  (9) 


889  (9) 

Maxima and Minima Using Lagrange Multipliers 


898  (10) 


908  (11) 

Double Integrals over Rectangular Regions 


919  (18) 

Important Terms and Symbols 


929  (1) 


930  (3) 

Group Activity 1: City Planning 


933  (1) 

Group Activity 2: Numerical Integration of Multivariable Functions 


934  (3) 
APPENDIX A Basic Algebra Review 

937  (68) 

SelfTest on Basic Algebra 


937  (2) 


939  (6) 

A2 Algebra and Real Numbers 


945  (7) 

A3 Operational on Polynomials 


952  (7) 

A4 Factoring Polynomials 


959  (6) 

A5 Operations on Rational Expressions 


965  (6) 

A6 Integer Exponents and Scientific Notation 


971  (6) 

A7 Rational Exponents and Radicals 


977  (7) 

A8 Linear Equations and Inequalities in One Variable 


984  (10) 


994  (11) 
APPENDIX B Special Topics 

1005  (20) 

B1 Sequences, Series, and Summation Notation 


1005  (7) 

B2 Arithmetic and Geometric Sequences 


1012  (8) 


1020  (5) 
APPENDIX C Tables 

1025  (1) 
APPENDIX B Table I 


Table I Basic Geometric Formulas 


1025  (2) 

Table II Integration Formulas 


1027  
Answers 

1  (1) 
Index 

1  