APPLIED CALCULUS, 3/E brings together the best of both new and traditional curricula to meet the needs of today's students. The author team's extensive teaching experience and proven ability to write innovative and relevant problems has made this text a true bestseller. Exciting new real-world applications make this new edition even more meaningful to students in management, life and social sciences. This book will work well for those departments seeking a middle ground for their instructors.

APPLIED CALCULUS, 3/E exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.

APPLIED CALCULUS, 3/E exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.

1 FUNCTIONS AND CHANGE 1

1.1 WHAT IS A FUNCTION? 2

1.2 LINEAR FUNCTIONS 6

1.3 RATES OF CHANGE 14

1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS 22

1.5 EXPONENTIAL FUNCTIONS 33

1.6 THE NATURAL LOGARITHM 40

1.7 EXPONENTIAL GROWTH AND DECAY 44

1.8 NEW FUNCTIONS FROM OLD 52

1.9 PROPORTIONALITY, POWER FUNCTIONS, AND POLYNOMIALS 56

1.10 PERIODIC FUNCTIONS 64

REVIEW PROBLEMS 71

PROJECTS: COMPOUND INTEREST, POPULATION CENTER OF THE US 77

FOCUS ON MODELING 78

FITTING FORMULAS TO DATA 78

COMPOUND INTEREST AND THE NUMBER e 86

FOCUS ON THEORY 92

LIMITS TO INFINITY AND END BEHAVIOR 92

2 RATE OF CHANGE: THE DERIVATIVE 97

2.1 INSTANTANEOUS RATE OF CHANGE 98

2.2 THE DERIVATIVE FUNCTION 106

2.3 INTERPRETATIONS OF THE DERIVATIVE 111

2.4 THE SECOND DERIVATIVE 119

2.5 MARGINAL COST AND REVENUE 125

REVIEW PROBLEMS 130

PROJECTS: ESTIMATING THE TEMPERATURE OF A YAM, TEMPERATURE AND ILLUMINATION

133

FOCUS ON THEORY 135

LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE 135

Preface xvii

3 SHORT-CUTS TO DIFFERENTIATION 141

3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS 142

3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 148

3.3 THE CHAIN RULE 153

3.4 THE PRODUCT AND QUOTIENT RULES 158

3.5 DERIVATIVES OF PERIODIC FUNCTIONS 162

REVIEW PROBLEMS 166

PROJECTS: CORONER’S RULE OF THUMB, AIR PRESSURE AND ALTITUDE 169

FOCUS ON THEORY 170

ESTABLISHING THE DERIVATIVE FORMULAS 170

FOCUS ON PRACTICE 173

173

4 USING THE DERIVATIVE 175

4.1 LOCAL MAXIMA AND MINIMA 176

4.2 INFLECTION POINTS 182

4.3 GLOBAL MAXIMA AND MINIMA 188

4.4 PROFIT, COST, AND REVENUE 195

4.5 AVERAGE COST 202

4.6 ELASTICITY OF DEMAND 208

4.7 LOGISTIC GROWTH 213

4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION 221

REVIEW PROBLEMS 227

PROJECTS: AVERAGE AND MARGINAL COSTS, FIREBREAKS, PRODUCTION AND THE PRICE OF

RAW MATERIALS 232

5 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL 235

5.1 DISTANCE AND ACCUMULATED CHANGE 236

5.2 THE DEFINITE INTEGRAL 242

5.3 THE DEFINITE INTEGRAL AS AREA 249

5.4 INTERPRETATIONS OF THE DEFINITE INTEGRAL 254

5.5 THE FUNDAMENTAL THEOREM OF CALCULUS 262

REVIEW PROBLEMS 266

PROJECTS: CARBON DIOXIDE IN POND WATER, FLOODING IN THE GRAND CANYON 269

xviii Preface

FOCUS ON THEORY 271

THEOREMS ABOUT DEFINITE INTEGRALS 271

6 USING THE DEFINITE INTEGRAL 275

6.1 AVERAGE VALUE 276

6.2 CONSUMER AND PRODUCER SURPLUS 280

6.3 PRESENT AND FUTURE VALUE 286

6.4 INTEGRATING RELATIVE GROWTH RATES 289

REVIEW PROBLEMS 294

PROJECTS: DISTRIBUTION OF RESOURCES, YIELD FROM AN APPLE ORCHARD 296

7 ANTIDERIVATIVES 299

7.1 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY 300

7.2 INTEGRATION BY SUBSTITUTION 304

7.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS 308

7.4 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY 313

REVIEW PROBLEMS 319

PROJECTS: QUABBIN RESERVOIR 321

FOCUS ON PRACTICE 322

322

8 PROBABILITY 323

8.1 DENSITY FUNCTIONS 324

8.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY 328

8.3 THE MEDIAN AND THE MEAN 335

REVIEW PROBLEMS 340

PROJECTS: TRIANGULAR PROBABILITY DISTRIBUTION 341

9 FUNCTIONS OF SEVERAL VARIABLES 343

9.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES 344

Preface xix

9.2 CONTOUR DIAGRAMS 348

9.3 PARTIAL DERIVATIVES 360

9.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY 368

9.5 CRITICAL POINTS AND OPTIMIZATION 373

9.6 CONSTRAINED OPTIMIZATION 378

REVIEW PROBLEMS 387

PROJECTS: A HEATER IN A ROOM, OPTIMIZING RELATIVE PRICES FOR ADULTS AND CHILDREN,

MAXIMIZING PRODUCTION AND MINIMIZING COST: “DUALITY” 391

FOCUS ON THEORY 392

DERIVING THE FORMULA FOR A REGRESSION LINE 392

10 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS 397

10.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION 398

10.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS 402

10.3 SLOPE FIELDS 406

10.4 EXPONENTIAL GROWTH AND DECAY 412

10.5 APPLICATIONS AND MODELING 417

10.6 MODELING THE INTERACTION OF TWO POPULATIONS 427

10.7 MODELING THE SPREAD OF A DISEASE 432

REVIEW PROBLEMS 436

PROJECTS: HARVESTING AND LOGISTIC GROWTH, POPULATION GENETICS, THE SPREAD OF

SARS 438

FOCUS ON THEORY 441

SEPARATION OF VARIABLES 441

11 GEOMETRIC SERIES 445

11.1 GEOMETRIC SERIES 446

11.2 APPLICATIONS TO BUSINESS AND ECONOMICS 451

11.3 APPLICATIONS TO LIFE SCIENCES 455

REVIEW PROBLEMS 460

PROJECTS: DO YOU HAVE ANY COMMON ANCESTORS?, HARROD-HICKS MODEL OF AN EXPANDING

NATIONAL ECONOMY, PROBABILITY OF WINNING IN SPORTS 461

APPENDIX: SPREADSHEET PROJECTS 463

SPREADSHEET PROJECTS 464

1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY 464

2. CREDIT CARD DEBT 465

3. CHOOSING A BANK LOAN 466

4. COMPARING HOME MORTGAGES 467

5. PRESENT VALUE OF LOTTERY WINNINGS 468

6. COMPARING INVESTMENTS 468

7. INVESTING FOR THE FUTURE: TUITION PAYMENTS 469

8. NEW OR USED? 469

9. VERHULST: THE LOGISTIC MODEL 470

10. THE SPREAD OF INFORMATION: A COMPARISON OF TWO MODELS 471

11. THE FLU IN WORLD WAR I 471

INDEX 501