Preface 

xi  
CHAPTER R ALGEBRA REFERENCE 



xvi  


xix  


xxii  


xxv  


xxxi  


xxxvi  


xli  
CHAPTER 1 FUNCTIONS 


1.1 Lines and Linear Functions 


2  (17) 

1.2 The Least Squares Line 


19  (12) 

1.3 Properties of Functions 


31  (13) 

1.4 Quadratic Functions; Translation and Reflection 


44  (10) 

1.5 Polynomial and Rational Functions 


54  (14) 


68  (7) 

1.7 Extended Application: Using Extrapolation to Predict Life Expectancy 


75  (2) 
CHAPTER 2 EXPONENTIAL LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS 


2.1 Exponential Functions 


77  (12) 

2.2 Logarithmic Functions 


89  (14) 

2.3 Applications: Growth and Decay 


103  (6) 


109  (17) 

Summary of Important Functions 


126  (2) 


128  (5) 

Extended Application: Characteristics of the Monkeyface Prickleback 


133  (2) 
CHAPTER 3 THE DERIVATIVE 



135  (19) 


154  (8) 


162  

3.4 Definition of the Derivative 


113  (77) 

3.5 Graphical Differentiation 


190  (1) 


191  (12) 
CHAPTER 4 CALCULATING THE DERIVATIVE 


4.1 Techniques for Finding Derivatives 


203  (8) 

4.2 Derivatives of Products and Quotients 


211  (12) 


223  (11) 

4.4 Derivatives of Exponential Functions 


234  (8) 

4.5 Derivatives of Logarithmic Functions 


242  (8) 

4.6 Derivatives of Trigonometric Functions 


250  (9) 

Rules for Derivatives Summary 


259  (1) 


260  (6) 
CHAPTER 5 GRAPHS AND THE DERIVATIVE 


5.1 Increasing and Decreasing Functions 


266  


218  (72) 

5.3 Higher Derivatives, Concavity, and the Second Derivative Test 


290  (16) 


306  (10) 


316  (6) 
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE 



322  (9) 

6.2 Applications of Extrema 


331  (11) 

6.3 Implicit Differentiation 


342  (7) 


349  (7) 

6.5 Differentials: Linear Approximation 


356  (7) 


363  (4) 

Extended Application: A Total Cost Model for a Training Program 


367  (2) 
CHAPTER 7 INTEGRATION 



369  (11) 


380  (9) 

7.3 Area and the Definite Integral 


389  (14) 

7.4 The Fundamental Theorem of Calculus 


403  (11) 

7.5 Integrals of Trigonometric Functions 


414  (5) 

7.6 The Area Between Two Curves 


419  (7) 


426  (2) 


428  (5) 

Extended Application: Estimating Depletion Dates for Minerals 


433  
CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION 


8.1 Numerical Integration 


431  (15) 


446  (10) 

8.3 Volume and Average Value 


456  (7) 


463  (6) 


469  (3) 

Extended Application: Flow Systems 


472  (4) 
CHAPTER 9 MULTIVARIABLE CALCULUS 


9.1 Functions of Several Variables 


476  (13) 


489  (11) 


500  (9) 

9.4 Total Differentials and Approximations 


509  (5) 


514  (7) 


521  (10) 

Extended Application: Optimization for a Predator 


531  (3) 
CHAPTER 10 MATRICES 



534  (18) 

10.2 Addition and Subtraction of Matrices 


552  (9) 

10.3 Multiplication of Matrices 


561  (12) 


573  (11) 

10.5 Eigenvalues and Eigenvectors 


584  (11) 


595  (6) 

Extended Application: Contagion 


601  (2) 
CHAPTER 11 DIFFERENTIAL EQUATIONS 


11.1 Solutions of Elementary and Separable Differential Equations 


603  (13) 

11.2 Linear FirstOrder Differential Equations 


616  (7) 


623  (7) 

11.4 Linear Systems of Differential Equations 


630  (9) 

11.5 Nonlinear Systems of Differential Equations 


639  (7) 

11.6 Applications of Differential Equations 


646  (6) 


652  (4) 

Extended Application: Pollution of the Great lakes 


656  (3) 
CHAPTER 12 PROBABILITY 



659  (15) 

12.2 Introduction to Probability 


674  (17) 

12.3 Conditional Probability; Independent Events; Bayes' Theorem 


691  (18) 

12.4 Discrete Random Variables; Applications to Decision Making 


709  (12) 


721  (1) 


722  (5) 

Extended Application: Medical Diagnosis 


727  (2) 
CHAPTER 13 PROBABILITY AND CALCULUS 


13.1 Continuous Probability Models 


729  (9) 

13.2 Expected Value and Variance of Continuous Random Variables 


738  

13.3 Special Probability Density Functions 


146  (614) 


760  (5) 

Extended Application: Exponential Waiting Times 


765  
TABLES 


Table 1 Formulas from Geometry 


A1  

Table 2 Area Under a Normal Curve 


A2  


A4  

Table 4 Integrals Involving Trigonometric Functions 


A5  
Answers to Selected Exercises 

A7  
Photo Acknowledgments 

A49  
Index of Applications 

I1  
Index 

I7  