Applied calculus /
Applied calculus /
Deborah Hughes-Hallett ...[et al.] ; with the assistance of Otto K. Bretscher ... [et al.]
- 3rd ed.
- Hoboken, N. J. : Wiley, 2006.
- xx, 506 p. : ill. ; 27 cm.
Previous ed.: 2003. Ill. on inside covers.
Includes index.
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.
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.
0471681210 9780471681212
Calculus
QA303 / .H354 2006
Previous ed.: 2003. Ill. on inside covers.
Includes index.
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.
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.
0471681210 9780471681212
Calculus
QA303 / .H354 2006