Table of Contents
PREFACE IX
INDEX OF APPLICATIONS XIII
CHAPTER 1
FUNCTIONS 1
1.1 Functions, Graphs, and Tables, 1
1.2 Graphing Utilities, 9
1.3 Functions and Graphs in Applications, 20
1.4 Linear Functions, 30
1.5 Other Important Functions, 44
1.6 Operations on Functions, 51
CHAPTER 2
THE DERIVATIVE 59
2.1 The Slope of a Curve at a Point, 59
2.2 The Derivative as a Rate of Change, 69
2.3 The Derivative Function, 83
2.4 Describing Graphs of Functions, 94
2.5 The First and Second Derivative Rules, 108
2.6 Limits and the Derivative, 119
2.7 Differentiability and Continuity, 129
CHAPTER 3
ALGEBRAIC DIFFERENTIATION AND ITS APPLICATIONS 137
3.1 Some Rules for Differentiation, 137
3.2 More About Derivatives, 145
3.3 Obtaining Graphs of Functions (Introduction), 153
3.4 Obtaining Graphs of Functions (Conclusion), 159
3.5 Optimization Problems, 167
3.6 Further Optimization Problems, 175
3.7 Applications of Calculus to Business and Economics, 185
CHAPTER 4
EXPONENTIAL AND LOGARITHMIC FUNCTIONS 195
4.1 The Exponential Function e^{x} , 195
4.2 The Product and Quotient Rules, 204
4.3 The Chain Rule, 212
4.4 The Natural Logarithm Function, 217
4.5 The Derivative of ln x, 223
4.6 Properties of the Natural Logarithm Function, 228
CHAPTER 5
APPLICATIONS OF THE EXPONENTIAL AND
LOGARITHMIC FUNCTIONS 235
5.1 Exponential Growth and Decay, 236
5.2 Compound Interest, 252
5.3 Applications of the Natural Logarithm Function to Economics, 261
CHAPTER 6
ANTIDIFFERENTIATION AND DIFFERENTIAL EQUATIONS 271
6.1 Antidifferentiation, 271
6.2 Differential Equations, 280
6.3 Qualitative Theory of Autonomous Differential Equations, 286
6.4 Applications of Autonomous Differential Equations, 296
CHAPTER 7
THE DEFINITE INTEGRAL 309
7.1 Areas and Riemann Sums, 310
7.2 The Definite Integral, 320
7.3 Areas in the xyPlane, 331
7.4 Applications of the Definite Integral, 339
7.5 The Fundamental Theorem of Calculus, 348
7.6 Techniques of Integration, 357
7.7 Improper Integrals, 367
7.8 Applications of Calculus to Probability, 374
CHAPTER 8
FUNCTIONS OF SEVERAL VARIABLES 383
8.1 Examples of Functions of Several Variables, 383
8.2 Partial Derivatives, 391
8.3 Maxima and Minima of Functions of Several Variables, 403
8.4 Lagrange Multipliers and Constrained Optimization, 414
APPENDICES 427
A Using Visual Calculus Software, 427
B Solving Quadratic Equations, 433
C Using the TI82 Graphing Calculator: A Summary, 439
D Using the TI83 Graphing Calculator: A Summary, 446
E Using the TI85 Graphing Calculator: A Summary, 453
ANSWERS TO ODDNUMBERED EXERCISES 459
INDEX 483
