Perface 

ix  
Introduction 

1  (2) 


3  (58) 

0.1 Functions and Their Graphs 


3  (15) 

0.2 Some Important Functions 


18  (9) 

0.3 The Algebra of Functions 


27  (4) 

0.4 Zeros of FunctionsThe Quadratic Formula and Factoring 


31  (9) 

0.5 Exponents and Power Functions 


40  (7) 

0.6 Functions and Graphs in Applications 


47  (14) 


61  (70) 

1.1 The Slope of a Straight Line 


62  (10) 

1.2 The Slope of a Curve at a Point 


72  (6) 


78  (9) 

1.4 Limits and the Derivative 


87  (11) 

1.5 Differentiability and Continuity 


98  (5) 

1.6 Some Rules for Differentiation 


103  (7) 

1.7 More About Derivatives 


110  (5) 

1.8 The Derivative as a Rate of Change 


115  (16) 

2 Applications of the Derivative 


131  (72) 

2.1 Describing Graphs of Functions 


131  (13) 

2.2 The First and Second Derivative Rules 


144  (10) 

2.3 Curve Sketching (Introduction) 


154  (8) 

2.4 Curve Sketching (Conclusion) 


162  (7) 

2.5 Optimization Problems 


169  (9) 

2.6 Further Optimization Problems 


178  (9) 

*2.7 Applications of Calculus to Business and Economics 


187  (16) 

3 Techniques of Differentiation 


203  (28) 

3.1 The Product and Quotient Rules 


203  (8) 

3.2 The Chain Rule and the General Power Rule 


211  (6) 

3.3 Implicit Differentiation and Related Rates 


217  (14) 

4 The Exponential and Natural Logarithm Functions 


231  (30) 

4.1 Exponential Functions 


231  (4) 

4.2 The Exponential Function e(x) 


235  (6) 

4.3 Differentiation of Exponential Functions 


241  (5) 

4.4 The Natural Logarithm Function 


246  (5) 

4.5 The Derivative of In x 


251  (4) 

4.6 Properties of the Natural Logarithm Function 


255  (6) 

5 Applications of the Exponential and Natural Logarithm Functions 


261  (40) 

5.1 Exponential Growth and Decay 


262  (10) 


272  (8) 

*5.3 Applications of the Natural Logarithm Function to Economics 


280  (6) 

*5.4 Further Exponential Models 


286  (15) 


301  (56) 


302  (9) 

6.2 Areas and Riemann Sums 


311  (10) 

6.3 Definite Integrals and the Fundamental Theorem 


321  (11) 

6.4 Areas in the xyPlane 


332  (10) 

6.5 Applications of the Definite Integral 


342  (15) 

7 Functions of Several Variables 


357  (54) 

7.1 Examples of Functions of Several Variables 


357  (7) 


364  (11) 

7.3 Maxima and Minima of Functions of Several Variables 


375  (8) 

7.4 Lagrange Multipliers and Constrained Optimization 


383  (11) 

*7.5 The Method of Least Squares 


394  (7) 


401  (10) 

8 The Trigonometric Functions 


411  (32) 

8.1 Radian Measure of Angles 


411  (4) 

8.2 The Sine and the Cosine 


415  (9) 

8.3 Differentiation of sin t and cost 


424  (10) 

8.4 The Tangent and Other Trigonometric Functions 


434  (9) 

9 Techniques of Integration 


443  (46) 

9.1 Integration by Substitution 


445  (6) 


451  (5) 

9.3 Evaluation of Definite Integrals 


456  (5) 

*9.4 Approximation of Definite Integrals 


461  (12) 

*9.5 Some Applications of the Integral 


473  (5) 


478  (11) 

10 Differential Equations 


489  (46) 

10.1 Solutions of Differential Equations 


489  (7) 

*10.2 Separation of Variables 


496  (9) 

*10.3 Numerical Solution of Differential Equations 


505  (7) 

10.4 Qualitative Theory of Differential Equations 


512  (10) 

10.5 Applications of Differential Equations 


522  (13) 

11 Taylor Polynomials and Infinite Series 


535  (46) 


535  (9) 

*11.2 The NewtonRaphson Algorithm 


544  (9) 


553  (10) 

*11.4 Series with Positive Terms 


563  (7) 


570  (11) 

12 Probability and Calculus 


581  

12.1 Discrete Random Variables 


581  (8) 

12.2 Continuous Random Variables 


589  (10) 

12.3 Expected Value and Variance 


599  (6) 

12.4 Exponential and Normal Random Variables 


605  (11) 

12.5 Poisson and Geometric Random Variables 


616  
Appendices 

A1  
A Calculus and the TI82 Calculator 

A1  
B Calculus and the TI83 Calculator 

A6  
C Calculus and the TI85 Calculator 

A11  
D Calculus and the TI86 Calculator 

A16  
E Areas Under the Standard Normal Curve 

A22  
Answers to Exercises 

A23  
Index 

I1  

*Sections preceded by a * are optional in the sense that they are not prerequisites for later material. 

