Preface 

ix  
Student and Instructor Resources 

xv  

Part One A Library of Elementary Functions 


1  (128) 

A Beginning Library of Elementary Functions 


2  (76) 


3  (18) 

Elementary Functions: Graphs and Transformations 


21  (14) 

Linear Functions and Straight Lines 


35  (18) 


53  (25) 

Important Terms, Symbols, and Concepts 


68  (2) 


70  (5) 

Group Activity 1: Introduction to Regression Analysis 


75  (1) 

Group Activity 2: Mathematical Modeling in Business 


76  (2) 

Additional Elementary Functions 


78  (51) 

Polynomial and Rational Functions 


79  (16) 


95  (14) 


109  (20) 

Important Terms, Symbols, and Concepts 


122  (1) 


123  (3) 

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


126  (1) 

Group Activity 2: Comparing Regression Models 


126  (3) 

Part Two Finite Mathematics 


129  (840) 


130  (50) 


131  (8) 


139  (13) 

Future Value of an Annuity; Sinking Funds 


152  (9) 

Present Value of an Annuity; Amortization 


161  (19) 

Important Terms, Symbols, and Concepts 


174  (1) 


175  (3) 

Group Activity 1: Reducing Interest Payments on a Home Mortgage 


178  (1) 

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


178  (2) 

Systems of Linear Equations; Matrices 


180  (94) 

Review: Systems of Linear Equations in Two Variables 


182  (14) 

Systems of Linear Equations and Augmented Matrices 


196  (9) 

GaussJordan Elimination 


205  (15) 

Matrices: Basic Operations 


220  (14) 

Inverse of a Square Matrix 


234  (11) 

Matrix Equations and Systems of Linear Equations 


245  (10) 

Leontief InputOutput Analysis 


255  (19) 

Important Terms, Symbols, and Concepts 


264  (3) 


267  (4) 

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


271  (1) 

Group Activity 2: Direct and Indirect Operating Costs 


272  (2) 

Linear Inequalities and Linear Programming 


274  (100) 

Systems of Linear Inequalities in Two Variables 


275  (14) 

Linear Programming in Two Dimensions: Geometric Approach 


289  (14) 

Geometric Introduction to the Simplex Method 


303  (8) 

Simplex Method: Maximization with Problem Constraints of the Form ≤ 


311  (19) 

Dual Problem: Minimization with Problem Constraints of the Form ≥ 


330  (16) 

Maximization and Minimization with Mixed Problem Constraints 


346  (28) 

Important Terms, Symbols, and Concepts 


364  (4) 


368  (3) 

Group Activity 1: TwoPhase Method: Alternative to the Big M Method 


371  (2) 

Group Activity 2: Production Scheduling 


373  (1) 

Logic, Sets, and Counting 


374  (46) 


375  (10) 


385  (6) 

Basic Counting Principles 


391  (10) 

Permutations and Combinations 


401  (19) 

Important Terms, Symbols, and Concepts 


414  (1) 


415  (2) 

Group Activity 1: Combinations with Repetition Allowed 


417  (1) 

Group Activity 2: Subset Lattices of Finite Sets 


418  (2) 


420  (72) 

Sample Spaces, Events, and Probability 


422  (15) 

Union, Intersection, and Complement of Events; Odds 


437  (14) 

Conditional Probability, Intersection, and Independence 


451  (16) 


467  (7) 

Random Variable, Probability Distribution, and Expected Value 


474  (18) 

Important Terms, Symbols, and Concepts 


484  (1) 


485  (4) 

Group Activity 1: Car and Crying Towels 


489  (1) 

Group Activity 2: Simulation: Draft Lottery for Professional Sports 


490  (2) 


492  (48) 

Properties of Markov Chains 


493  (13) 


506  (11) 


517  (23) 

Important Terms, Symbols, and Concepts 


533  (1) 


534  (3) 

Group Activity 1: Social Mobility 


537  (1) 

Group Activity 2: Gambler's Ruin 


538  (2) 




540  (94) 


542  (16) 


558  (12) 


570  (16) 

Power Rule and Basic Differentation Properties 


586  (10) 

Derivatives of Products and Quotients 


596  (8) 

General Power Rule (Chain Rule) 


604  (8) 

Marginal Analysis in Business and Economics 


612  (22) 

Important Terms, Symbols, and Concepts 


623  (3) 


626  (5) 

Group Activity 1: Minimal Average Cost 


631  (1) 

Group Activity 2: Numerical Differentiation on a Graphing Utility 


632  (2) 

Graphing and Optimization 


634  (80) 

First Derivative and Graphs 


635  (18) 

Second Derivative and Graphs 


653  (16) 

Graphing Rational Functions 


669  (16) 

Absolute Maxima and Minima 


685  (7) 


692  (22) 

Important Terms, Symbols, and Concepts 


706  (3) 


709  (3) 

Group Activity 1: Maximizing Profit 


712  (1) 

Group Activity 2: Minimizing Construction Costs 


712  (2) 

Additional Derivative Topics 


714  (64) 

The Constant e and Continuous Compound Interest 


715  (8) 

Exponential Functions and Their Derivatives 


723  (11) 

Logarithmic Functions and Their Derivatives 


734  (13) 

Chain Rule: Elasticity of Demand 


747  (12) 


759  (7) 


766  (12) 

Important Terms, Symbols, and Concepts 


773  (1) 


774  (2) 

Group Activity 1: Increasing Production of Cellular Phones 


776  (1) 

Group Activity 2: Point of Diminishing Returns 


777  (1) 


778  (74) 

Antiderivatives and Indefinite Integrals 


779  (14) 

Integration by Substitution 


793  (12) 

Differential Equations; Growth and Decay 


805  (11) 


816  (11) 

The Fundamental Theorem of Calculus 


827  (25) 

Important Terms, Symbols, and Concepts 


841  (2) 


843  (4) 

Group Activity 1: Simpson's Rule 


847  (3) 

Group Activity 2: BellShaped Curves 


850  (2) 

Additional Integration Topics 


852  (46) 


853  (11) 

Applications in Business and Economics 


864  (12) 


876  (7) 


883  (15) 

Important Terms, Symbols, and Concepts 


892  (1) 


893  (2) 

Group Activity 1: Analysis of Income Concentration from Raw Data 


895  (1) 

Group Activity 2: Grain Exchange 


896  (2) 


898  (71) 

Functions of Several Variables 


899  (10) 


909  (10) 


919  (9) 

Maxima and Minima Using Lagrange Multipliers 


928  (10) 


938  (11) 

Double Integrals Over Rectangular Regions 


949  (20) 

Important Terms, Symbols, and Concepts 


960  (2) 


962  (2) 

Group Activity 1: City Planning 


964  (1) 

Group Activity 2: Numerical Integration of Multivariable Functions 


965  (4) 


969  (1) 

A SelfTest on Basic Algebra 


969  (64) 


971  (6) 

Operations on Polynomials 


977  (8) 


985  (7) 

Operations on Rational Expressions 


992  (6) 

Integer Exponents and Scientific Notation 


998  (6) 

Rational Exponents and Radicals 


1004  (7) 

Linear Equations and Inequalities in One Variable 


1011  (10) 


1021  (12) 


1033  (20) 

Sequences, Series, and Summation Notation 


1033  (7) 

Arithmetic and Geometric Sequences 


1040  (8) 


1048  (5) 


1053  (1) 

Table I Basic Geometric Formulas 


1053  (2) 

Table II Integration Formulas 


1055  
Answers 

1  (1) 
Index 

1  