
Straight Lines and Linear Functions 


2  (76) 

The Cartesian Coordinate System 


4  (9) 


13  (20) 

Using Technology: Graphing a Straight Line 


30  (3) 

Linear Functions and Mathematical Models 


33  (14) 


37  (7) 

Using Technology: Evaluating a Function 


44  (3) 

Intersection of Straight Lines 


47  (14) 

Using Technology: Finding the Points of Intersection of Two Graphs 


58  (3) 

The Method of Least Squares (Optional) 


61  (15) 

Using Technology: Finding an Equation of a LeastSquares Line 


68  (5) 

Summary of Principal Formulas and Terms 


73  (1) 


74  (2) 

Systems of Linear Equations and Matrices 


76  (104) 

Systems of Linear EquationsIntroduction 


78  (9) 

Solving Systems of Linear Equations I 


87  (19) 

Using Technology: Solving Systems of Linear Equations I 


102  (4) 

Solving Systems of Linear Equations II 


106  (13) 

Using Technology: Solving Systems of Linear Equations II 


116  (3) 


119  (13) 

Using Technology: Matrix Addition and Subtraction, Scalar Multiplication, and the Transpose of a Matrix 


130  (2) 

Multiplication of Matrices 


132  (16) 

Using Technology: Matrix Multiplication 


144  (4) 

The Inverse of a Square Matrix 


148  (17) 

Using Technology: Finding the Inverse of a Square Matrix 


160  (5) 

Leontief InputOutput Model (Optional) 


165  (15) 

Using Technology: The Leontief InputOutput Model 


172  (5) 

Summary of Principal Formulas and Terms 


177  (1) 


178  (2) 

Linear Programming: A Geometric Approach 


180  (38) 

Graphing Systems of Linear Inequalities in Two Variables 


182  (9) 

Linear Programming Problems 


191  (10) 

Portfolio: Leanne Jenkins 


198  (3) 

Graphical Solution of Linear Programming Problems 


201  (17) 

Summary of Principal Terms 


216  (1) 


216  (2) 

Linear Programming: An Algebraic Approach 


218  (48) 

The Simplex Method: Standard Maximization Problems 


220  (26) 

Portfolio: Harley Lance Kaplan 


241  (1) 

Using Technology: The Simplex Method: Solving Maximization Problems 


242  (4) 

The Simplex Method: Standard Minimization Problems 


246  (20) 

Using Technology: The Simplex Method: Solving Minimization Problems 


260  (4) 

Summary of Principal Terms 


264  (1) 


264  (2) 


266  (52) 


268  (14) 

Using Technology: Finding the Accumulated Amount of an Investment and Finding the Effective Rate of Interest 


280  (2) 


282  (12) 

Using Technology: Finding the Amount of an Annuity 


292  (2) 

Amortization and Sinking Funds 


294  (12) 


300  (4) 

Using Technology: Amortizing a Loan 


304  (2) 

Arthmetic and Geometric Progressions (Optional) 


306  (12) 

Summary of Principal Formulas and Terms 


315  (1) 


316  (2) 


318  (48) 


320  (12) 

The Number of Elements in a Finite Set 


332  (7) 

The Multiplication Principle 


339  (6) 

Portfolio: John L. Higgins 


342  (3) 

Permutations and Combinations 


345  (21) 

Using Technology: Evaluating n!, P(n, r), and C(n, r) 


360  (2) 

Summary of Principal Formulas and Terms 


362  (1) 


363  (3) 


366  (96) 

Experiments, Sample Spaces, and Events 


368  (10) 

Definition of Probability 


378  (11) 


389  (10) 

Use of Counting Techniques in Probability 


399  (9) 

Conditional Probability and Independent Events 


408  (16) 


424  (11) 


435  (27) 

Using Technology: Finding Distribution Vectors 


454  (4) 

Summary of Principal Formulas and Terms 


458  (1) 


459  (3) 

Probability Distributions and Statistics 


462  (76) 

Distributions of Random Variables 


464  (12) 

Using Technology: Graphing a Histogram 


472  (4) 


476  (15) 

Portfolio: Lilli Meiselman 


489  (2) 

Variance and Standard Deviation 


491  (13) 

Using Technology: Finding the Mean and Standard Deviation 


502  (2) 

The Binomial Distribution 


504  (12) 


516  (10) 

Applications of the Normal Distribution 


526  (12) 

Summary of Principal Formulas and Terms 


535  (1) 


536  (2) 


538  (32) 


540  (4) 


544  (9) 


553  (8) 

Inequalities and Absolute Value 


561  (9) 

Summary of Principal Formulas and Terms 


567  (1) 


568  (2) 

Functions, Limits, and the Derivative 


570  (122) 

Functions and Their Graphs 


572  (21) 

Using Technology: Graphing a Function 


588  (5) 


593  (9) 

Portfolio: Michael Marchlik 


598  (4) 

Functions and Mathematical Models 


602  (18) 

Using Technology: Finding the Points of Intersection of Two Graphs and Modeling 


614  (6) 


620  (25) 

Using Technology: Finding the Limit of a Function 


640  (5) 

OneSided Limits and Continuity 


645  (20) 

Using Technology: Finding the Points of Discontinuity of a Function 


660  (5) 


665  (27) 

Using Technology: Graphing a Function and Its Tangent Lines 


686  (3) 

Summary of Principal Formulas and Terms 


689  (1) 


689  (3) 


692  (94) 

Basic Rules of Differentiation 


694  (14) 

Using Technology: Finding the Rate of Change of a Function 


702  (6) 

The Product and Quotient Rules 


708  (13) 

Using Technology: The Product and Quotient Rules 


718  (3) 


721  (13) 

Using Technology: Finding the Derivative of a Composite Function 


728  (6) 

Marginal Functions in Economics 


734  (16) 


750  (9) 

Using Technology: Finding the Second Derivative of a Function at a Given Point 


756  (3) 

Implicit Differentiation and Related Rates 


759  (12) 


771  (15) 

Using Technology: Finding the Differential of a Function 


780  (3) 

Summary of Principal Formulas and Terms 


783  (1) 


784  (2) 

Applications of the Derivative 


786  (96) 

Applications of the First Derivative 


788  (23) 

Using Technology: Using the First Derivative to Analyze a Function 


806  (5) 

Applications of the Second Derivative 


811  (20) 

Using Technology: Finding the Inflection Points of a Function 


828  (3) 


831  (20) 

Using Technology: Analyzing the Properties of a Function 


844  (7) 


851  (16) 

Using Technology: Finding the Absolute Extrema of a Function 


864  (3) 


867  (15) 

Summary of Principal Terms 


879  (1) 


879  (3) 

Exponential and Logarithmic Functions 


882  (58) 


884  (14) 

Portfolio: Misato Nakazaki 


895  (1) 


896  (2) 


898  (8) 

Differentiation of Exponential Functions 


906  (13) 


916  (3) 

Differentiation of Logarithmic Functions 


919  (8) 

Exponential Functions as Mathematical Models 


927  (13) 

Summary of Principal Formulas and Terms 


938  (1) 


939  (1) 


940  (102) 

Antiderivatives and the Rules of Integration 


942  (15) 

Integration by Substitution 


957  (11) 

Area and the Definite Integral 


968  (11) 

The Fundamental Theorem of Calculus 


979  (14) 

Using Technology: Evaluating Definite Integrals 


990  (3) 

Evaluating Definite Integrals 


993  (12) 

Using Technology: Evaluating Definite Integrals for PiecewiseDefined Functions 


1002  (3) 


1005  (16) 

Using Technology: Finding the Area Between Two Curves 


1018  (3) 

Applications of the Definite Integral to Business and Economics 


1021  (21) 

Using Technology: Consumers' Surplus and Producers' Surplus 


1035  (2) 

Summary of Principal Formulas and Terms 


1037  (1) 


1038  (4) 

Additional Topics in Integration 


1042  (52) 


1044  (7) 


1051  (17) 

Portfolio: James H. Chesebro 


1066  (2) 


1068  (11) 

Applications of Probability to Calculus 


1079  (15) 

Summary of Principal Formulas and Terms 


1090  (2) 


1092  (2) 

Calculus of Several Variables 


1094  (75) 

Functions of Several Variables 


1096  (10) 


1106  (18) 

Using Technology: Finding Partial Derivatives at a Given Point 


1120  (4) 

Maxima and Minima of Functions of Several Variables 


1124  (11) 

Constrained Maxima and Minima and the Method of Lagrange Multipliers 


1135  (13) 


1148  (21) 

Summary of Principal Terms 


1165  (1) 


1165  (4) 
Appendix A The System of Real Numbers 

1169  (4) 
Appendix B Tables 

1173  (6) 

Table 1: Binomial Probabilities 


1174  (3) 

Table 2: The Standard Normal Distribution 


1177  (2) 
Answers to OddNumbered Exercises 

1179  (56) 
Index 

1235  